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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