Answers edited by Timber Lin

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• Does anybody know how to solve the limit of #(x^x-x^{x^2})/(1-x)^2# when #x->1# ?
  
• What is the fourth root of 1296?
  
• What is the equation of the line tangent to # f(x)=(-x^2-1)/(x+4) # at # x=5 #?
  
• Find the arc length of the function #y=1/2(e^x+e^-x)# with parameters #0\lex\le2#?
  
• Find the interval & radius of convergence for the power series in #1b?
  
• Using the graph of #f(x) = 2x^3 + x^2 - 3x+1#, what is the average rate of change from #x=-2# to #x=0#?
  
• 2. Find the first 3 terms of the Taylor series for 𝑓(𝑥) = sin 𝜋𝑥 centered at 𝑎 = 0.5. Use your answer to find an approximate value to 𝑠𝑖𝑛 (𝜋/2+𝜋/10). How to do?
  
• How do you differentiate #x^7 - 8xy + y^4 = 7#?
  
• A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 50 ft from the pole?