Answers edited by Luke Phillips

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• If #a_k in RR^+# and #s = sum_(k=1)^na_k#. Prove that for any #n > 1# we have #prod_(k=1)^n(1+a_k) < sum_(k=0)^n s^k/(k!)#?
  
• How do you integrate #int x^3/sqrt(64+x^2)# by trigonometric substitution?
  
• Question #cc2a5
  
• How do you use substitution to integrate # x/sqrt(x+4) dx#?
  
• Question #ea9c6
  
• Let F(x) be the cdf of the continuous-type random variable X, and assume that F(x)=0 for x<=0 and 0<F(x),1 for 0<x. Prove that if P(X>x+y|X>x)=P(X>y), then F(x)=1-#e^(-lamdax# , 0<x ?
  
• Question #297a6
  
• What are the critical points of #f(x) =1/(xe^x)-e^(2x)/x#?
  
• What is the derivative of #tan^2(sinx)#?
  
• How do you find #lim sqrt(x^2+1)-x# as #x->oo#?
  
• Question #30055
  
• Show that #sum x/2^x = 2# summation running 0 to infinity ?
  
• Integrate 1/(1+bcotx)?
  
• Question #a39e8
  
• What is the purpose of the Gamma function?
  
• How to determine complex numbers that satisfy relation:#abs(z)^2-2iz+2a(1+i)=0;a>0#?
  
• What is #int (x^3-2x^2+6x+9 ) / (2x^2- x +3 )#?
  
• Question #5b41a
  
• How do you solve #\sin \frac { 2x + 1} { x } + \sin \frac { 2x + 1} { 3x } - 3\cos ^ { 2} \frac { 2x + 1} { 3x } = 0#?
  
• Question #23877
  
• If we were to toss a single die (singular for dice) 1000 times, how many 6s could we expect over the long run? What is the standard deviation?
  
• Question #2d31f
  
• Evaluate the integral #int \ sqrt(x-x^2)/x \ dx #?
  
• Question #518f9
  
• #lim_(xto1) (sinpix)/(x-1)# ?
  
• Question #ededb
  
• What is the derivative of this function #y=(cos^-1(4x^2))^2#?