# Homework Help

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• Math
`r=1-sin theta` To solve, express the polar equation in parametric form. To convert it to parametric equation, apply the formula `x = rcos theta` `y=r sin theta` Plugging in `r=1-sin theta` , the...

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• Math
The formula of arc length of a parametric equation on the interval `alt=tlt=b` is: `L = int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt` The given parametric equation is: `x=t` `y=t^5/10 + 1/(6t^3)` The...

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• Math
The equation for arc length in parametric coordinates is: `L=int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt` Where in this case: `dx/dt=d/dt (t^(1/2))=1/2t^(-1/2)` `dy/dt=d/dt(3t-1)=3` `a=0, b=1` Therefore...

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• Math
Arc length of a curve C described by the parametric equations x=f(t) and y=g(t), `a<=t<=b` where f' and g' are continuous on [a,b] and C is traversed exactly once as t increases from a to b,...

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• Math
The formula of arc length of a parametric equation on the interval `alt=tlt=b` is: `L = int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt` The given parametric equation is: `x = e^(-t)cost` `y=e^(-t)sint` The...

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• Math
The formula of arc length of a parametric equation on the interval `alt=tlt=b` is: `L = int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt` The given parametric equation is: `x=6t^2` `y=2t^3` The derivative of...

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• Math
The formula of arc length of a parametric equation on the interval `alt=tlt=b` is: `L = int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt` The given parametric equation is: `x=3t + 5` `y=7 - 2t` The derivative...

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• Math
`x=cos^2 theta` `y=cos theta` First, take the derivative of x and y with respect to theta . `dx/(d theta) = 2costheta (-sin theta)` `dx/(d theta)=-2sintheta cos theta` `dy/(d theta) = -sin theta`...

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• Math
`x=sec theta` `y=tan theta` First, take the derivative of x and y with respect to theta. `dx/(d theta) = sec theta tan theta` `dy/(d theta) = sec^2 theta` Then, set each derivative equal to zero....

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• Math
`x=5+3cos theta` `y= -2+sin theta` First, take the derivative of x and y with respect to theta. `dx/(d theta) = -3sin theta` `dy/(d theta) = cos theta` Take note that the slope of a tangent is...

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• Math
`x=3cos theta` `y=3sin theta` First, take the derivative of x and y with respect to `theta` . `dx/(d theta) = -3sin theta` `dy/(d theta) = 3cos theta` Take note that the slope of a tangent is equal...

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• Math
Parametric curve (x(t),y(t)) has a horizontal tangent when its slope `dy/dx` is zero, i.e. `dy/dt=0` and `dx/dt!=0` . Curve has a vertical tangent if its slope approaches infinity i.e. `dx/dt=0`...

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• Math
Parametric curve (x(t),y(t)) has a horizontal tangent if its slope `dy/dx` is zero, i.e when `dy/dt=0` and `dx/dt!=0` Curve has a vertical tangent line, if its slope approaches infinity i.e...

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• Math
Parametric curve (x(t),y(t)) has a horizontal tangent if its slope `dy/dx` is zero i.e. when `dy/dt=0` and `dx/dt!=0` It has a vertical tangent, if its slope approaches infinity i.e. `dx/dt=0` and...

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• Math
Parametric curve has a horizontal tangent if its slope `dy/dx` is zero i.e. when `dy/dt=0` and `dx/dt!=0` Tangent line is vertical if its slope approaches infinity i.e. `dx/dt=0` and `dy/dt!=0`...

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• Math
The parametric equations are: `x=t^3-6t` ------------------(1) `y=t^2` -----------------(2) From equation 2, `t=+-sqrt(y)` Substitute `t=sqrt(y)` in equation (1),...

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• Math
Given parametric equations are: `x=t^2-t` `y=t^3-3t-1` We have to find the point where the curves cross. Let's draw a table for different values of t, and find different values of t which give the...

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• Math
Given parametric equations are: `x=2sin(2t)` `y=3sin(t)` Let's make a table of x and y values for different values of t. (Refer the attached image).The point where the curve crosses itself will...

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• Math
Given parametric equations are : `x=t-3` ----------------(1) `y=t/(t-3)` ----------------(2) Draw a table for different values of t and plot the points obtained from the table.(Refer the...

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• Math
`x=sqrt(t)` ----------------(1) `y=t-5` -----------------(2) Draw a table for different values of t and plot the points obtained from the table.(Refer the attached image). Connect the points to...

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• Math
The graph is described by the parametric equations in x, y and t: `x(t) = t^2 + t, quad y(t) = t^2 - t ` A sketch of the graph is as pictured, with (as standard) the horizontal axis being the...

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• Math
`x=t^3` -----------------(1) `y=t^2/2` -----------------(2) Draw a table for different values of t and plot the points obtained from the table.Connect the points to a smooth curve.( Refer the...

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• Math
` x = 2t^2, quad y = t^4 + 1 ` ` <br> ` ` ` The graph described by the pair of equations in x, y and t is given above. Written in the form of those two equations, the graph is expressed in...

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• Math
`x=1+t` --------------(1) `y=t^2` -------------(2) Draw a table for different values of t and plot the points obtained from the table (Refer the attached image). Connect the points to...

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• Math
`x = 5-4t` `y=2+5t` To graph a parametric equation, assign values to t. Since there is no given interval for t, let's consider the values from t=-3 to t=3. t=-3 `x=5-4(-3) = 17` `y= 2+5(-3) = -13`...

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• Math
`x=2t-3` ----------------------(1) `y=3t+1` ----------------------(2) From equation 1, `x+3=2t` `=>t=(x+3)/2` Plug in the value of t in equation (2) `y=3((x+3)/2)+1` `y=(3x+9)/2+1`...

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• Math
From the table of power series, we have: `(1+x)^k = 1 +kx+ (k(k-1))/2! x^2 +(k(k-1)(k-2))/3!x^3 +` ... To apply this on the given integral `int_0^0.2 sqrt(1+x^2)dx` , we let: `sqrt(1+x^2)...

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• Math
From the table of power series, we have: `(1+x)^k = 1 +kx+ (k(k-1))/2! x^2 +(k(k-1)(k-2))/3!x^3 +` ... To apply this on the given integral `int_0.1^0.3 sqrt(1+x^3)dx` , we let: `sqrt(1+x^3)...

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• Math
From a table of power series, recall that we have: `arctan(x) = sum_(n=0)^oo (-1)^n x^(2n+1)/(2n+1)` To apply this on the given problem, we replace the "`x` " with "`x^2` ". We get: `arctan(x^2)...

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• Math
From the Power Series table for trigonometric function, we have: `arctan(x) =sum_(n=0)^oo (-1)^n x^(2n+1)/(2n+1)` `= x -x^3/3 +x^5/5 - x^7/7 + x^9/9-...` Applying it on the...

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• Math
From the table of power series, we have: `cos(x) = sum_(n=0)^oo (-1)^nx^(2n)/(2n)!` `= 1-x^2/(2!)+x^4/(4!)-x^6/(6!)+` ... To apply this on the given integral `int_0^1 cos(x^2) dx` ,...

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• Math
From the Power Series table for trigonometric function, we have: `sin(x) =sum_(n=0)^oo (-1)^n x^(2n+1)/((2n+1)!)` `= x -x^3/(3!) +x^5/(5!) - x^7/(7!) +...` Applying it on the integral...

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• Math
From the basic list of power series, we have: `ln(x) =sum_(n=0)^oo (-1)^(n) (x-1)^(n+1)/(n+1)` `= (x-1)-(x-1)^2/2+(x-1)^3/3 -(x-1)^4/4 +...` We replace "`x` " with "`x+1` " to setup:...

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• Math
From the table of power series, we have: `e^x = sum_(n=0)^oo x^n/n! ` `= 1+x+x^2/(2!)+x^3/(3!)+x^4/(4!)+x^5/(5!)+` ... To apply this on the given integral `int_0^1 e^(-x^2)dx` , we replace...

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• Math
Maclaurin series is a special case of Taylor series which is centered at a=0. We follow the formula: `f(x) =sum_(n=0)^oo (f^n(0))/(n!)x^n` or `f(x) = f(0) +...

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• Math
Maclaurin series is a special case of Taylor series which is centered at a=0. We follow the formula: `f(x) =sum_(n=0)^oo (f^n(0))/(n!)x^n` or `f(x) = f(0) +...

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• Math
A binomial series is an example of infinite series. It is a series that is only convergent when we have `|x|lt1` and with a sum of `(1+x)^k ` where k is any number. To apply binomial series in...

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• Math
A binomial series is an example of infinite series. When we have a function of `f(x) = (1+x)^k` such that k is any number and convergent to `|x| lt1` , we may apply the sum of series as the value...

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• Math
Binomial series is an example of an infinite series. When it is convergent at `|x|lt1` , we may follow the sum of the binomial series as `(1+x)^k` where k is any number. The formula will be:...

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• Math
Recall binomial series follows: `(1+x)^k=sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!)x^n` or `(1+x)^k = 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3 +(k(k-1)(k-2)(k-3))/(4!)x^4+...` To...

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• Math
Recall a binomial series follows: `(1+x)^k=sum_(n=0)^oo _(k(k-1)(k-2)...(k-n+1))/(n!)x^n` or `(1+x)^k = 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3 +(k(k-1)(k-2)(k-3))/(4!)x^4+` ... To...

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• Math
Binomial series is an example of an infinite series. When it is convergent at `|x|lt1` , we may follow the sum of the binomial series as `(1+x)^k` where `k` is any number. The formula will be:...

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• Math
Recall binomial series that is convergent when `|x|lt1` follows: `(1+x)^k=sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!)x^n` or `(1+x)^k = 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3...

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• Math
Binomial series is an example of an infinite series. When it is convergent at `|x|lt1` , we may follow the sum of the binomial series as `(1+x)^k` where `k` is any number. We may follow the...

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• Math
Recall binomial series that is convergent when `|x|lt1` follows: `(1+x)^k=sum_(n=0)^oo _(k(k-1)(k-2)...(k-n+1))/(n!)` or`(1+x)^k= 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3...

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• Math
Recall binomial series that is convergent when `|x|lt1` follows: `(1+x)^k=sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!)x^n` or `(1+x)^k= 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3...

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• Math
Taylor series is an example of infinite series derived from the expansion of `f(x) ` about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c` . The general formula for...

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• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at` x=c` . The general formula for...

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• Math
aylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c` . The general formula for...

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