Answers created by Luke Phillips

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• How do you find the limit of `(1 - 1/x)^x` as x approaches infinity?
  
• `lim_(xto1) (sinpix)/(x-1)` ?
  
• Question #23877
  
• How do you use substitution to integrate `x/sqrt(x+4) dx`?
  
• A solid is formed by attaching a hemisphere to each end of a cylinder. If the total volume is to be 120cm^3, find the radius (in cm) of the cylinder that produces the minimum surface area. Express your answer correct to 2 decimal places. Help!?
  
• Integrate 1/(1+bcotx)?
  
• What is the derivative of `tan^2(sinx)`?
  
• How do you solve this ? `lim_(x->0^+)(1+sin(4x))^cot(x)`
  
• What is the derivative of this function `y=(cos^-1(4x^2))^2`?
  
• Question #d6553
  
• Question #5b41a
  
• Question #baaae
  
• How to stay motivated to study maths and what are some good websites for practice (High school level)?
  
• Question #ea9c6
  
• Show that `sum x/2^x = 2` summation running 0 to infinity ?
  
• Question #5fb99
  
• Question #d76e9
  
• Find the derivative implicity if x = tan xy. Help!?
  
• Can a complex number be written Cartesian form in terms of i to a power other than 1? And if so...
  
• Question #2d31f
  
• How do you find the probability of no successes when `n` independent Bernoulli trials are carried out with probability of success `p`?
  
• 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?
  
• How do you solve `\sin \frac { 2x + 1} { x } + \sin \frac { 2x + 1} { 3x } - 3\cos ^ { 2} \frac { 2x + 1} { 3x } = 0`?
  
• What is the period of `f(theta) = tan ( ( 17 theta)/12 )- cos ( ( 3 theta)/ 4 )`?
  
• Question #7cb01
  
• Question #297a6
  
• Evaluate the integral `int \ sqrt(x-x^2)/x \ dx`?
  
• How do you find the derivative of `2^arcsin(x)`?
  
• How do you find the derivative of `log_5(arctanx^x)`?
  
• What is the Maclaurin series for `ln(5-x)`?
  
• Question #4d1ca
  
• 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!)`?
  
• What is the purpose of the Gamma function?
  
• How do you integrate the following integral?
  
• Question #ededb
  
• Evaluate `int \ (1+sqrt(x))^9/sqrt(x) \ dx`?
  
• How do you integrate `int x^3/sqrt(64+x^2)` by trigonometric substitution?
  
• Question #caa80
  
• 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 ?
  
• We have `f:RR->RR,f(x)=1/(1+x^2)` and `I_n=int_0^1f^n(x)dx,ninNN`. Prove that `2nI_(n+1)=(2n-1)I_n+1/(2^n),ninNN`*?
  
• What's the integral of `int tan(x)^4 dx`?
  
• Question #30055
  
• Question #53d06
  
• How do you find `lim sqrt(x^2+1)-x` as `x->oo`?
  
• How do you find the derivative of `u=e^(e^x)`?
  
• What is `int (x^3-2x^2+6x+9 ) / (2x^2- x +3 )`?
  
• Question #cc2a5
  
• Question #a39e8
  
• How do you calculate `abs(-3+2i)`?
  
• Question #7e404
  
• What is the derivative of `x^(3/x)`?
  
• What are the critical points of `f(x) =1/(xe^x)-e^(2x)/x`?
  
• Question #800f5
  
• Question #518f9
  
• How do I solve this using l'hopital's rule rule ? `y=(sin2x)^(tan3x)`
  
• How do you find `\int _ { 0} ^ { x } \frac { \sin ( t ) } { t } d t`?
  
• How do you find vertical, horizontal and oblique asymptotes for `[(e^-x)(x^5) + 2] /[ x^5 - x^4 -x +1]`?
  
• How to determine complex numbers that satisfy relation:`abs(z)^2-2iz+2a(1+i)=0;a>0`?
  
• Question #dbf40