Math at eNotes
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The latest questions and answers, from members following Math at eNotes.Sat, 29 Aug 2015 08:10:02 PSTen-usThe slope of tangent to `y=e^xcosx` at (0,1) = `dy/dx` at (0,1) `dy/dx...
http://www.enotes.com/homework-help/y-e-x-cos-x-0-1-find-an-equation-tangent-line-493741
The slope of tangent to `y=e^xcosx` at (0,1) = `dy/dx` at (0,1) `dy/dx = e^x(cosx-sinx)` Slope is equal to 1. The equation of the tangent is equal to `y-1=1(x-0).` That is `x-y+1=0.` ``http://www.enotes.com/homework-help/y-e-x-cos-x-0-1-find-an-equation-tangent-line-493741Sat, 29 Aug 2015 08:10:02 PSTThe slope of the tangent is equal to the derivative of the equation of...
http://www.enotes.com/homework-help/y-sec-x-pi-3-2-find-an-equation-tangent-line-493740
The slope of the tangent is equal to the derivative of the equation of the curve at the given point. `dy/dx = secx.tanx` The slope of the tangent is equal to `2sqrt3.` The equation of the tangent is equal to `y-2=2sqrt3(x-pi/3)` that is `2sqrt3x-y=(2pi)/sqrt3-2` ``http://www.enotes.com/homework-help/y-sec-x-pi-3-2-find-an-equation-tangent-line-493740Sat, 29 Aug 2015 08:04:53 PSTThe slope of the tangent = `dy/dx` at (pi,-1). `dy/dx = -sinx-cosx` The...
http://www.enotes.com/homework-help/y-cos-x-sin-x-pi-1-find-an-equation-tangent-line-493742
The slope of the tangent = `dy/dx` at (pi,-1). `dy/dx = -sinx-cosx` The slope of the tangent is equal to 1. The equation of the tangent is `y-(-1)=1(x-pi)` . that is `x-y=pi+1` ``http://www.enotes.com/homework-help/y-cos-x-sin-x-pi-1-find-an-equation-tangent-line-493742Sat, 29 Aug 2015 07:59:15 PSTThe slope of the tangent is equal to the derivative of the equation of...
http://www.enotes.com/homework-help/y-x-tan-x-pi-pi-find-an-equation-tangent-line-493743
The slope of the tangent is equal to the derivative of the equation of the curve at the given point. `dy/dx = 1+sec^2x` Slope of the tangent is equal to 2 The equation of the tangent is equal to y-pi=2(x-pi) That is `2x-y-pi=0. ` `` ``http://www.enotes.com/homework-help/y-x-tan-x-pi-pi-find-an-equation-tangent-line-493743Sat, 29 Aug 2015 07:53:52 PSTThe equation of the tangent to the curve is y=2x and that of the normal...
http://www.enotes.com/homework-help/y-2-x-e-x-0-0-find-equations-tangent-line-normal-492736
The equation of the tangent to the curve is y=2x and that of the normal is y=-x/2http://www.enotes.com/homework-help/y-2-x-e-x-0-0-find-equations-tangent-line-normal-492736Sat, 29 Aug 2015 06:31:22 PSTPlease find attached a solution to the problem above.
http://www.enotes.com/homework-help/y-2-x-e-x-0-0-find-equations-tangent-line-normal-492736
Please find attached a solution to the problem above.http://www.enotes.com/homework-help/y-2-x-e-x-0-0-find-equations-tangent-line-normal-492736#1Sat, 29 Aug 2015 06:27:41 PSTintegration by substitution: `u=e^x` `du=e^x.dx` `dx=(du)/e^x=(du)/u` `...
http://www.enotes.com/homework-help/solve-integral-int-dx-sqrt-1-e-2x-436635
integration by substitution: `u=e^x` `du=e^x.dx` `dx=(du)/e^x=(du)/u` ` ` then, `=- sec h^-1(u) +C` ` ` `=-sec h^-1 (e^x) +C` i.e, `` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `` ` ` ` ` ` ` ` ` ` ` ` ` `http://www.enotes.com/homework-help/solve-integral-int-dx-sqrt-1-e-2x-436635Sat, 29 Aug 2015 04:08:46 PST`f(theta) = sec(theta)/(1 + sec(theta))` so, `f'(theta) = (sec(theta)/(1...
http://www.enotes.com/homework-help/f-theta-sec-theta-1-sec-theta-differentiate-493730
`f(theta) = sec(theta)/(1 + sec(theta))` so, `f'(theta) = (sec(theta)/(1 + sec(theta)))'` `= (1- (1/(1 + sec(theta))))'` `= 0 -(1/(1 + sec(theta)))'` `= - tan(theta)* sec(theta)/(1 + sec(theta))^2` ` =- tan(theta)/((1 + sec(theta))^2* cos(theta))`http://www.enotes.com/homework-help/f-theta-sec-theta-1-sec-theta-differentiate-493730Fri, 28 Aug 2015 16:21:27 PST`y = (t sin(t))/(1 + t)` `y' = ((t sin(t))/(1 + t))'` `= ((1+t)...
http://www.enotes.com/homework-help/y-t-sin-t-1-t-differentiate-493732
`y = (t sin(t))/(1 + t)` `y' = ((t sin(t))/(1 + t))'` `= ((1+t) *(d/(dt) (t sin t)) - t sint *(d/(dt) ( 1+t)))/(1+t)^2` `=(((1+t) *(t(cos t)+ sint)) - (t sint *(1)))/(1+t)^2` ` = (sin(t) +t(t+1)(cost))/(1+t)^2`http://www.enotes.com/homework-help/y-t-sin-t-1-t-differentiate-493732Fri, 28 Aug 2015 16:16:31 PSTBy sing the definition of the derivative, `lim_(h -> 0) [ cos(x + h)...
http://www.enotes.com/homework-help/prove-using-definition-derivative-that-f-x-cos-x-493739
By sing the definition of the derivative, `lim_(h -> 0) [ cos(x + h) - cos(x) ] / h` `=lim_(h -> 0)[ cos(x)cos(h) - sin(x)sin(h) - cos(x) ] / h` `=lim_(h -> 0)[ cos(x) [ cos(h) - 1 ] - sin(x)sin(h) ] / h` =`lim_(h -> 0)[ cos(x) [cos(h) - 1]/h ] - lim_(h -> 0) (sin(x)sin(h)/h)` =`cos(x)lim_(h -> 0)[ [cos(h) - 1]/h ] - sin(x)lim_(h -> 0) (sin(h)/h)` as `lim_(h -> 0)[ [cos(h) - 1]/h ] =0 ` and `lim_(h -> 0) (sin(h)/h) =...http://www.enotes.com/homework-help/prove-using-definition-derivative-that-f-x-cos-x-493739Fri, 28 Aug 2015 16:01:16 PSTy = x^2 sin(x) tan(x) to find y' so, y' = (x^2 sin(x) tan(x))' let a=...
http://www.enotes.com/homework-help/y-x-2-sin-x-tan-x-differentiate-493735
y = x^2 sin(x) tan(x) to find y' so, y' = (x^2 sin(x) tan(x))' let a= sin(x) tan(x) so, y' = (x^2 * a)' = x^2 (a)'+ a *(2x) where a' = ( sin(x) tan(x))' = sin(x) d/(dx) (tan(x))+ tan(x) d/(dx) (sin(x)) = sin(x) * sec^2(X) + tan(x) * cos(x) so, y' = x^2(sin(x) * sec^2(X) + tan(x) * cos(x)) +(sin(x) tan(x))(2x)http://www.enotes.com/homework-help/y-x-2-sin-x-tan-x-differentiate-493735Fri, 28 Aug 2015 15:51:33 PSTTo find `y'=d/(dx) x*e^x csc(x)` let `a= x*e^x` so, `y'=d/(dx)...
http://www.enotes.com/homework-help/f-x-x-e-x-csc-x-differentiate-493734
To find `y'=d/(dx) x*e^x csc(x)` let `a= x*e^x` so, `y'=d/(dx) (a*csc(x))` `= (d/(dx) a) *csc(x) + a* d/(dx)(csc(x))` substituting` a = x*e^x` so` a' = (d/(dx) a)` `= (d/(dx) x*e^x) = x*e^x + e^x` and `d/(dx)(csc(x)) = -csc(x)cot(x)` so , `y'=(d/(dx) a) *csc(x) + a* d/(dx)(csc(x))` `= (x*e^x + e^x)*csc(x) + (x*e^x)* (-csc(x)cot(x))` `= (e^x)(1+x)*csc(x)- (x*e^x)* (csc(x))*(cot(x))` `= (e^x)*csc(x)[(1+x)-x*(cot(x))]`http://www.enotes.com/homework-help/f-x-x-e-x-csc-x-differentiate-493734Fri, 28 Aug 2015 15:43:23 PSTThe slope of a line tangent to the curve y = f(x) at a point where x =...
http://www.enotes.com/homework-help/show-that-curve-y-2-e-x-3x-5x-3-has-no-tangent-494463
The slope of a line tangent to the curve y = f(x) at a point where x = a, is given by the value of f'(a). In the problem, the curve is represented by y = 2*e^x + 5x^3 + 3x. First determine the derivative `(dy)/(dx)` . `(dy)/(dx)= (2*e^x + 5x^3 + 3x)'` = `2*e^x + 15x^2 + 3` If a tangent to this curve has slope 2, the equation 2*e^x + 15x^2 + 3 = 2 should have a real root. 2*e^x + 15x^2 + 3 = 2 => 2*e^x + 15x^2 = 2 - 3 = -1 As e is positive,...http://www.enotes.com/homework-help/show-that-curve-y-2-e-x-3x-5x-3-has-no-tangent-494463Fri, 28 Aug 2015 05:06:53 PSTShow that the curve y = 2*e^x +3x + 5x^3 has no tangent line with slope 2.
http://www.enotes.com/homework-help/show-that-curve-y-2-e-x-3x-5x-3-has-no-tangent-494463
Show that the curve y = 2*e^x +3x + 5x^3 has no tangent line with slope 2.http://www.enotes.com/homework-help/show-that-curve-y-2-e-x-3x-5x-3-has-no-tangent-494463#2August 28, 2015, 4:52 am PSTQuotient Rule:...
http://www.enotes.com/homework-help/y-cos-x-1-sin-x-differentiate-493731
Quotient Rule: `y'=(((-sin(x))*(1-sin(x))-(-cos(x))(cos(x)))/((1-sin(x))^(2))) ` `y'=(((cos^(2)(x))+(sin(x))*(sin(x)-1))/((sin(x)-1)^(2))`http://www.enotes.com/homework-help/y-cos-x-1-sin-x-differentiate-493731Fri, 28 Aug 2015 01:19:55 PST