# Calculus Homework Help

### Showing All Questions Answered Popular Recommended Unanswered Editor's Choice in Calculus

• Math
The integral `int 1/(1+sqrt x) dx` has to be derived. `int 1/(1+sqrt x) dx` Let `x = u^2` `(dx)/(du) = 2u` `dx = 2u*du ` `int 1/(1+sqrt x) dx` = `int 1/(1+u) * 2u du` Let `1 + u = y => dy = du`...

Asked by lxsptter on via web

• Math
The definite integral `int_0^8 (1+x^2)/(x^3 + 3x) dx` has to be determined. First determine the integral `int (1+x^2)/(x^3 + 3x) dx` and find the value of the same between x = 0 and x = 8 `int...

Asked by lxsptter on via web

• Math
The y-intercept of the tangent to the curve y = e^x*sin x at the point where x = 0 has to be determined. For a curve y = f(x), the slope of the tangent to the curve at a point `(y_0, x_0)` is...

Asked by lxsptter on via web

• Math
To find the gradient or slope of the tangent line at a given point on the curve, we need to take the derivative of the equation of that curve, which gives the slope of the tangent line at any...

Asked by sherryseah on via web

• Math
`f(x)=ax^3+6x^2+bx+4` Differentiating with respect to x, `f'(x)=3ax^2+12x+b` Differentiating again with respect to x, `f''(x)=6ax+12` f has a relative minimum at x=-1 and a relative minimum at...

Asked by user2324274 on via web

• Math
The surface area of a closed cylinder is 100 cm^2. The material used to build this cylinder is used to create another cylinder such that the volume is maximized. Let the radius of the ends of the...

Asked by enotesenoter on via web

• Calculus
Given, velocity of water from the pipe, `v = 1064p^(1/2)` Differentiate both sides with respect to t, `(dv)/(dt)=1064*1/2*p^(-1/2)*(dp)/(dt)` `=532* p^(-1/2)*(dp)/(dt)` Put the given values:...

Asked by pphok on via web

• Calculus
A rectangular sheet of perimeter 27 cm and dimensions x cm by y cm is to be rolled into a cylinder. What values of x and y give the largest volume? Perimeter of rectangularsheet= 27 cm But...

Asked by pphok on via web

• Calculus
Let x be the distance of the man from the lamp post and y be the distance of the tip of his shadow from the lamp post (please refer to the attached image). Triangles `Delta SBL` and `DeltaHFL` are...

Asked by pphok on via web

• Calculus
Let h be the length (in inches) of the cutout portion of the square corners. Eventually, that would be the height of the cardboard box. Both sides of the cardboard would reduce by 2h, owing to the...

Asked by pphok on via web

• Calculus
The company wishes to manufacture a box with a volume of 44 cubic feet that is open on top and is twice as long as it is wide. Let the length of the box that uses minimum amount of material be L....

Asked by pphok on via web

• Calculus
Given equation of the curve is: `x^4y^4=16` Use implicit differentiation to solve for dy/dx: `d/(dx)(x^4y^4)=d/(dx)(16)` `rArr x^4*4y^3(dy)/(dx)+4x^3y^4=0` `rArr...

Asked by pphok on via web

• Calculus
A. Area=`int_(x=1)^(x=4)ydx` `=int_1^4 1/sqrt(x)dx` `={2sqrt(x)}_1^4` `=2(2-1)=2` `` Area is 2 square units. B. area=`int_1^3(x^2-3x+2)dx` `=(x^3/3-3x^2/2+2x)_1^3` `=(9-27/2+6)-(1/3-3/2+2)`...

Asked by amanda53 on via web

• Calculus
You need to evaluate the partial derivative `f_x` differentiate the given function with respect to x, considering y as constant, such that: `f_x = (del f(x,y))/(del x)` `f_x = 1/(sqrt(1 -...

Asked by subashchandar on via web

• Math
a) Using geometry, the object we wish to find the surface area of is a cone with no base and no 'nose' (a 'conical fustrum'). The formula for the surface area of this cone with no base and no...

Asked by maham4102 on via web

• Math
We are given the function `y = 3lnx - 3x^2` and asked to fund the number of extreme points. An extreme point is an absolute maximum or absolute minimum, absolute meaning that it is finite in...

Asked by ruals on via web

• Calculus
`f(x;y)=x/y` it's defined `D=<<AA x in RR >> xx<< AA y in RR | y!=0 >>` We se function is not limited for, x wit a finte value and y too much close to zero on the left...

Asked by user9055008 on via web

• Math
The antiderivative of a function is equivalent of the integral of that function. Therefore the antiderivative of `(x^2+2x+2)^(1/2)` with respect to `x` is equivalent to `int (x^2+2x+2)^(1/2)dx`...

Asked by rouche on via web

• Math
The formula for the volume of a sphere is `V = 4/3pir^3` Think of this as adding two hemispheres together, where each of those hemispheres is the sum of many many circle slices/discs from `x=0` ro...

Asked by nerdygirl-1996 on via web

• Calculus
1) a) `y = 3/x` , `x>0` The area under the graph is given by `int_0^infty 3/x dx = 3log(x)|_0^infty = 3[lim_(x-> infty)log(x) - lim_(x->0)log(x)] ` `= lim_(x-> infty) x` b) `y = 12x`,...

Asked by eddie1366 on via web

• Calculus
We know by defnition of inverse function. `f^(-1)(f(x))=x` Let `g=f^(-1)` ,then `g(f(x))=x` (i) differentiating (i) with respect to x ,implicitly `g'(f(x))f'(x)=1` `g'(f(x))=1/(f'(x)) ``(ii)`...

Asked by mohan1kumar on via web

• Math
`int_3^6 1/10x(6x^2-15)dx` First, factor out 1/10. `=1/10int_3^6x(6x^2-15)dx` Then, distribute x to (6x^2-15)dx. `=1/10int_3^6(6x^3-15x)dx` Then, integrate each term inside the parenthesis uisng...

Asked by gunn10 on via web

• Calculus
Hi, djshan, Sorry, but I'm not too sure what you want us to do here. Are we going to graph this? Find the intercepts? Find the zeros? Something else? I would assume we are graphing it. To...

Asked by djshan on via web

• Math
The solid takes the form of a scaled (by ` ``80pi`) bivariate bell (Normal/Gaussian) curve where the variance of the two variables `x` and `y` is `sigma^2 =2` and the correlation `rho=0` . Ignoring...

Asked by david3 on via web

• Math
We have the surface `f(x,y) = 64 + x^2 - y^2` and the constraint `x^2+y^2 <=1` , `x` and `y` `in R` This constraint can be rewritten as `x^2 = 1 - y^2` and `y^2 <=1` Substituting for...

Asked by ramiyaou on via web

• Math
I think you mean differential of y = x² sinx. First we find the derivative of sin2x. Using double angle formula sin2x= 2sinx.cosx, we get d(sin2x)/dx = d(2sinx cosx)/dx =...

Asked by ahmedmasoudi on via web

• Calculus
let x+1=t ,dx=dt , x^(n)=(t-1)^(n)=t^(n)-c(n,1)t^(n-1)(-1)+ c(n,2)t^(n-1)(-1)x^(2)+..............+c(n,n-1)t (-1)^(n-1)+ (-1)^(n) int(x^(n)/(x+1))dx=int (( t^(n)-c(n,1)t^(n-1)(-1)+...

Asked by user9880347 on via web

• Calculus
`int_0^1 x^n/(n+1)=x^(n+1)/(n+1)^2|_0^1=1/(n+1)^2` So your integral is equal to `1/(n+1)^2` which is less than `1/(n+1)` because n is a natural number. I'm sorry because the above formula is hard...

Asked by userwtf on via web

• Calculus
The integral `int (x*e^(2x))/(2x+1)^2 dx` has to be determined. Use integration by parts. Let `x*e^(2x) = u` `du = 2*x*e^(2x) + e^(2x) dx` =>` du = e^(2x)*(1 + 2x) dx` `dx/(2x+1)^2 = dv`...

Asked by user8052413 on via web

• Calculus
I'm assuming that when you say you have a graph you mean you have graphical representation (picture) of a function which by itself doesn't mean much (you can't do anything better than guessing)....

Asked by user129479 on via web

• Calculus
We have to find the value of lim x-->0+ [(x^x)^2)] lim x-->0+ [(x^x)^2)] => lim x-->0+ [e^(ln ((x^x)^2))] => lim x-->0+ [e^(ln ((x^2x))] => lim x-->0+ [e^(2x*ln x)] As the...

Asked by bpayne9171 on via web

• Calculus
We'll have to differentiate with respect to x, using the product rule: (u*v)' = u'*v + u*v' Let u = cos x and v = ln x y' = (cos x)'*(ln x) + (cos x)*(ln x)' y' = -sin x*ln x + (cos x)/x The first...

Asked by potziunea on via web

• Calculus
We'll re-write the given expression, isolating dy: dy = (3x^5 + 6e^2x)dx We'll integrate both sides: Int dy = Int (3x^5 + 6e^2x)dx We'll use the property of integral to be additive: Int dy = Int...

Asked by istetz on via web

• Calculus
Since the function that has to be differentiated is the result of composition of 2 functions, logarithmic and linear functions, we'll apply the chain rule and we'll differentiate with respect to...

• Calculus
We'll determine f(0). To get f(0), we'll replace x by 0 in the expression of f(x): f(0) = a*0^4 + b*0^2 +c f(0) = c But f(0) = 2 (from enunciation) => c = 2 Now, we'll calculate f'(x): f'(x) =...

Asked by frontman0 on via web

• Calculus
Int f(x)dx = Int dx/(x+2)(x+3) We'll apply Leibniz-Newton rule to calculate the definite integral. We'll decompose the fraction into partial fractions. 1/(x+2)(x+3) = A/(x+2) + B/(x+3) 1 = A(x+3) +...

Asked by boroboacana on via web

• Calculus
We'll differentiate the given function with respect to x: df/dx = d/dx {[3-(1/x)] / (x-1)} df/dx = d/dx [3/(x-1)] - d/dx [1/x(x-1)] d/dx [3/(x-1)] = [(x-1)*d/dx(3) - 3*d/dx(x-1)]/(x-1)^2 d/dx...

Asked by ginkomind on via web

• Calculus
We'll have to differentiate the given function y with respect to x. y = sin (cos x) We'll differentiate both sides: dy = [sin (cos x)]'dx We'll differentiate using chain rule, since the given...

Asked by olaf on via web

• Calculus
If we'll replace x by 0, we'll get the indetermination "0/0" type. Therefore, we can use L'Hospital's rule, to determine the limit of the quotient of derivatives. lim f(x)/g(x) = lim f'(x)/g'(x)...

Asked by aehtorod on via web

• Calculus
We'll have to apply product rule and chain rule to determine the 1st derivative of the given function: y' = (2x)'*ln(2x)*sin(2x) + (2x)*[ln(2x)]'*sin(2x) + (2x)*ln(2x)*[sin(2x)]' y' =...

Asked by carrotpie on via web

• Calculus
The dimensions of the rectangle, at the time t, are x and y cm. We'll compute the area of the rectangle, at the time t: A = x*y cm^2 (1) We'll have to determine dA/dt if we want to know how fast...

Asked by idaberg on via web

• Calculus
Let f(x) = x^x If we'll put x = 1 => f(1) = 1^1 =1 We'll re-write the function whose limit has to be found out: lim (f(x) - 1)/(x - 1) By definition, the derivative of a function f(x), at the...

Asked by sokolof on via web

• Calculus
The function f(x) = x^(sin x) Let y = f(x) = x^(sin x) Take the natural log of both the sides ln y = ln [ x^(sin x)] => ln y = sin x * ln x Differentiate both the sides with respect to x =>...

Asked by orlovolga on via web

• Calculus
To determine the primitive function y, we'll have to compute the indefinite integral of the function. If dy/dx = 1/sqrt(36-x^2) => dy = dx/sqrt[(6)^2 - x^2] We'll integrate both sides: Int dy =...

Asked by guteskind on via web

• Calculus
To determine the primitive function f(x), we must calculate the indefinite integral of f'(x). We'll apply substitution technique, replacing ln(2x+3) by t. ln(2x+3) = t We'll differentiate both...

Asked by brautjungfer on via web

• Calculus
We'll write the denominator as the result of expanding the square: x^2 + 4x + 4 = (x+2)^2 We'll re-write the integral: Int f(x)dx = Int dx/(x+2)^2 We'll use the techinque of changing the variable....

Asked by browntim3 on via web

• Calculus
I'll solve this problem, considering that the term "182"i s 1*2 (since the "*" symbol and the digit 8 are on the same key and the rest of the terms are written accordingly). The Stolz Cesaro...

Asked by nena1993 on via web

• Calculus
To determine the antiderivative of a given function, we'll have to calculate the indefinite integral of that function. We'll apply integration by parts. First, we'll recall the formula: Int udv =...

Asked by loochy on via web

• Calculus
We'll manage the right side of the expression and we'll differentiate tan(x/2). [tan(x/2)]' = 1/2*[cos(x/2)]^2 We'll re-write the expression: (1+sinx)/(1+cosx)=1/2*[cos(x/2)]^2 + tan(x/2) We'll...

Asked by oldcareer on via web

• Calculus
We have to find lim x--> inf. [(3x^2-4x+1)/(-8x^2+5)] substituting x = inf., gives the indeterminate form inf./inf., we can use l'Hopital's rule and substitute the numerator and denominator with...

Asked by sensitiv on via web