Answers created by Wataru

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• What is the antiderivative of `tan(x)`?
  
• How do you use the binomial series to expand `f(x)= 1/((1+x)^2)`?
  
• How do you find the equation of the tangent line to the curve `y=x^2e^-x` at (1, 1/e)?
  
• Find the length of the parametric curve `x = e^t + e^-t, y = 5 - 2t` from `t = 0 to t = 1`?
  
• Question #91038
  
• Question #1be07
  
• Does `a_n=x^n/(xn!)` converge for any x?
  
• Suppose `T_4(x) = 7-3(x-2)+7(x-2)^2-6(x-2)^3+8(x-2)^4` is the 4th-degree Taylor polynomial centered at `x=2` for some function f, what is the value of `f^((3))(2)`?
  
• Question #f6339
  
• Question #5f86e
  
• How do you solve `|- 3+ b | \leq 3`?
  
• How do you evaluate `\lim _ { x \rightarrow 0} \frac { \sin ^ { 3} 2x } { \sin ^ { 3} 3x }`?
  
• If `k != 0`, what is `\lim _ { x \rightarrow k } \frac { x ^ { 2} - k ^ { 2} } { x ^ { 2} - k x }`?
  
• How do you find the average rate of change of `h(x) = x^3 − 1/5e^x` from [0,1]?
  
• Question #cc8ed
  
• How do you derive the maclaurin series for `f(x)=ln(1+x)`?
  
• How do you evaluate `\sum _ { n = 1} ^ { \infty } 8( \frac { 1} { 2} ) ^ { k - 1}`?
  
• Question #88d11
  
• How do you use the squeeze theorem to show that `lim_(x to 0)x^4cos2x=0`?
  
• How do you show that the series `1/3-2/5+3/7-4/9+...+((-1)^(n-1)n)/(2n+1)+...` diverges?
  
• How do you evaluate `\int _ { \frac { 1} { 6} \pi } ^ { \frac { 1} { 3} \pi } 3\tan ^ { 2} x d x`?
  
• Question #6aa72
  
• How many subsets with three elements of `A={1,2,3,4,5,6}` containing element "1"?
  
• Question #f9b8d
  
• Question #1abd1
  
• Question #b9e60
  
• Could you please prove that `lim_(x rarr 0) sin(x)/x = 1` using the formal definition of limits?
  
• Question #7f415
  
• Question #3ade9
  
• How do you simplify `sqrt12+sqrt27-sqrt3`?
  
• How do you simplify `\frac { z } { ( z - 1) ^ { 2} } - \frac { 1} { ( z - 1) ( z + 3) }`?
  
• How do you factor: `y= 32x^3 - 4`?
  
• How do you solve `|x + 3| = (x-2)`?
  
• How do you solve `32n+46=1+8n`?
  
• What is the second derivative of `f(x)=x/(x^2+1)`?
  
• Question #65c13
  
• Question #984b4
  
• Question #b5a4d
  
• How would you find the volume bounded by the coordinate planes and by the plane 3x + 2y + 2z = 6?
  
• How do you graph `y=sin^-1x` over the interval `-1<=x<=1`?
  
• If `f(x) = x^2-4` and `g` is a differentiable function of `x`, what is the derivative of `f(g(x))`?
  
• How do you differentiate `f(x) = x^3sqrt(7x+1)` using the product rule?
  
• What is the value of `\lim _ { x \rightarrow - 3} \frac { x ^ { 2} - 9} { x ^ { 2} - 2x - 15}`?
  
• What is an antiderivative of `3sec^2x + 2`?
  
• How do you find the second derivative of `sin(2x)`?
  
• How do you find the exact values of the sine, cosine, and tangent of the angle `(13pi)/12`?
  
• How do you find the area of the surface generated by rotating the curve about the y-axis `y=1/4x^4+1/8x^-2, 1<=x<=2`?
  
• Question #eb959
  
• How do you integrate `int (6(5 - x))/( (x - 7)(4 - x))` using partial fractions?
  
• What is the derivative of this function `sin^-1 (5x)`?
  
• If `f(x)= 3x^3-2` and `g(x) = e^(2x`, what is `f'(g(x))`?
  
• If `y^3+y=x^2`, what is `(dy)/(dx)`?
  
• What is the equation of the line that goes through `(3, -6)` and is parallel to the line `3x+y-10=0`?
  
• What is the derivative of `y= (5x)/sqrt (x^2+9)`?
  
• How do you differentiate `f(x) = 4/sqrt(tan^3(1/x)` using the chain rule?
  
• How to solve this limit?`lim_(x->oo)(xa^(x+1)+1);ain(0,1)`
  
• How do you simplify `(-5)^-2`?
  
• How do you differentiate `y=sin^-1(3x^5+1)^3`?
  
• The temperature drops from 48°C to 21°C in 9 hours. What is the average temperature change per hour?
  
• How do you graph the equation `y=-3`?
  
• How do you write 0.6% as a fraction?
  
• How do you prove that the `lim_(x to -2)(x^2 -5) = -1` using the formal definition of a limit?
  
• Let `a` is `real` and `epsilon>0`. Given `V_epsilon(a)={x : |x-a|<epsilon}`. How to find `gamma>0` so that `V_gamma(a)=V_epsilon(a)nnV_delta(a)` ?
  
• How do you differentiate `y = ((sin(x))^6 (tan(x))^2) / (x^2 + 2)^2`?
  
• How do you find the exact value of `tan(sin^-1(0.1))`?
  
• What are the critical values, if any, of `f(x) = xe^(2x)`?
  
• How do you find the derivative of `sqrtx+sqrty=9`?
  
• What is the sum of this geometric series. `sum2(3)^( n-1)` for n=1 to 6?
  
• How to prove that `{1/2^n}` is bounded series ?
  
• What is the derivative of `x(6^(-2x))`?
  
• How do you find `int(x^2-1/x^2+root3x)dx`?
  
• Let `a` is `real` and `epsilon>0`. Given `V_epsilon(a)={x : |x-a|<epsilon}`. How to find `gamma>0` so that `V_gamma(a)=V_epsilon(a)nnV_delta(a)` ?
  
• How do you solve `3\ln ( x - 5) = - 3`?
  
• What is `int tan^3(x)*sec(x)dx`?
  
• Question #03e6a
  
• How do you differentiate `f(x)= ( x + 1 )/ ( secx )` using the quotient rule?
  
• What is the equation of the tangent line of `f(x) =sqrt(ln(sinx))` at `x = pi/4`?
  
• How do you find the limits of `lim root(3)t +12t-2t^2 where t = -oo`?
  
• How do you evaluate limits of `lim 9/(x-3)^2` where x-3?
  
• What is the Cartesian form of `( 6 , ( - 16pi)/3 )`?
  
• Question #4f2f7
  
• How do you find the derivative of `ln(ln(3x))`?
  
• How do you use the limit comparison test to determine if `Sigma tan(1/n)` from `[1,oo)` is convergent or divergent?
  
• How do you find the derivative of `s=tan^2t`?
  
• A soccer ball kicked at the goal travels in a path given by the parametric equations: x=50t; `y=-16t^2+32t`, Suppose the ball enters the goal at a height of 5ft. How far away from the goal was the kicker?
  
• How do you use implicit differentiation to find dy/dx given `tanx+csc2y=1`?
  
• Use the principle of mathematical induction to prove that?: See picture
  
• What is the equation of the line that is normal to `f(x)= x/e^(2x-2)` at `x= 1`?
  
• Question #f6a18
  
• How do you find the linearization at a=1 of `f(x) = 2 ln(x)`?
  
• Question #b399e
  
• Question #3ded9
  
• How do you find the limit of `ln(sinx)` as `x->0^-`?
  
• How do you determine if the series the converges conditionally, absolutely or diverges given `Sigma (cos(npi))/(n+1)` from `[1,oo)`?
  
• The terminal side of `theta` in standard position contains (5,12), how do you find the exact values of the six trigonometric functions of `theta`?
  
• How do you find the period of `h(t) = 4*sin(3t) + 3*sin(tsqrt3)`?
  
• How do you find the inverse of `f(x) = 6x^3 - 3`?
  
• How many ways can 14 books be organized on a shelf?
  
• What is the integral of `ln(x+1)`?
  
• What is the integral of `sec^3(x)`?
  
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