Answers created by sente

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• Do there exist primes `a, b, c` satisfying `a^2+b^3=c^4`?
  
• Consider the sequence 1, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, ... What is its 2016th term?
  
• How do you solve `abs(x-a)<=a`?
  
• Question #e8695
  
• How does the profile of the ground have to be, to be able to drive with triangular wheels (equilateral) and without bumps?
  
• Can you use mathematical induction to prove that `t_n >= t_(n-1)` for all `n in ZZ^+` for a sequence with the general term: `t_n=(3n+5)/(n+2), n in ZZ^+`?
  
• Question #7cc9a
  
• Does `int_1^oo1/root(3)(x+1)dx` converge or diverge? If it converges, what is the integral?
  
• Question #29a12
  
• Can you use mathematical induction to prove that the sequence defined by `t_1=6` , `t_(n+1)= t_n/(3n` for all `n in ZZ^+` can be written as `t_n=18/(3^n(n-1)!` for all `n in ZZ^+`?
  
• Suppose that `f:RR->RR` has the properties `(a)` `|f(x)| le 1, forall x in RR` `(b)` `f(x+13/42)+f(x)=f(x+1/6)+f(x+1/7), forall x in RR` Prove that `f` is periodic?
  
• How do you test for convergence of `Sigma (-1)^n/sqrt(lnn)` from `n=[3,oo)`?
  
• Can you use mathematical induction to prove that `2^n > 4n` for all `n in ZZ^+ n>=5`?
  
• What is the LCM of `z^7-18z^6+81z^5, 5z^2-405` and `2z+18`?
  
• Question #2cc45
  
• Question #93699
  
• What is 30% of 400?
  
• How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given `(1-1/2)+(1/2-1/6)+(1/6-1/24)+...+(1/(n!)-1/((n+1)!))+...`?
  
• 8 is what percent of 40?
  
• Question #919b3
  
• Answer is 4 which order to solve? `3^0 (5^0 - 6^-1 * 3)/ 2^-1` I don't know if I should bring the `6^-1` down first or multiply by 3 first.
  
• How do you integrate `int sqrtxlnx` by integration by parts method?
  
• How do you test the series `Sigma 1/(nsqrtn)` from n is `[1,oo)` for convergence?
  
• How do you integrate by substitution `int x/(sqrt(1-x^2) dx`?
  
• Question #85951
  
• How do you find the product `(3c+4d)^2`?
  
• `y_n=log x_n, n =2,3,4,...and y_n-(n-1)/n y_(n-1)=1/n log n`, with `y_2=log sqrt2`, how do you prove that `x_n=(n!)^(1/n)`?
  
• What is the derivative of `f(x)=e^(x^2lnx)`?
  
• Question #b2dc7
  
• How do you solve `sqrt(x+7) = x-5` and find any extraneous solutions?
  
• How do you find `dy/dx` by implicit differentiation of `x^2+y^2=36`?
  
• How do you simplify `[(2xy^3)^2]^3`?
  
• How do you prove that the limit of `(x+3)=5` as x approaches 2 using the epsilon delta proof?
  
• Question #05911
  
• Find the limit... ?
  
• How do you prove that the limit `(x^2) = 4` as x approaches 2 using the formal definition of a limit?
  
• Question #4d4db
  
• How do you find the prime factorization on 75?
  
• How do you find a polynomial function that has zeros 0, 10?
  
• How do you solve by factoring and using the principle of zero products: `64v^2=36`?
  
• What is the difference between an explicit and recursive formula?
  
• Question #54f6a
  
• Question #95828
  
• How do you differentiate `y = e^(-2x + x^2)`?
  
• Question #c86dc
  
• Question #c86dc
  
• Question #a1e8f
  
• Question #94a46
  
• How do you solve and write the following in interval notation: `4+abs(3x+2) <=5`?
  
• Question #0426c
  
• How do you solve `lnx-ln5=0`?
  
• How do you find the derivative of `y=sqrtx/x`?
  
• How do you determine whether x-1 is a factor of the polynomial `x^3-3x^2+4x-2`?
  
• How do you solve `5A+7=3A+7+2A`?
  
• How do you use the epsilon delta definition to prove that the limit of `x^2-4` as `x->2`?
  
• Prove? `cscx(1+cosx)(cscx-cotx)=1`
  
• How do you solve `4^x=13`?
  
• How do you add `\frac { x } { x + 3} + \frac { 6x - 2} { x - 3}`?
  
• If `A= <-5 ,3 ,-3 >` and `B= <2 ,2 ,8 >`, what is `A*B -||A|| ||B||`?
  
• How do you differentiate `y=sin(e^x)`?
  
• The sum of a positive integer and its square is 90. What is the number?
  
• What is the length of side BC of the triangle? Explain how you arrived at your answer.
  
• How do you solve `x^3>=9x^2`?
  
• Question #5d572
  
• How do you evaluate the limit `e^(-x)/x` as x approaches `oo`?
  
• Question #828cc
  
• Question #828cc
  
• How do you integrate `int sec^3xtanx`?
  
• How do you find the range of `h(x)=x^2 -4` for the domain (-2,0,3,8)?
  
• What is the difference between squaring `sqrt(x-1)` and `sqrtx -1`?
  
• How do you find the derivative of `arctan(e^x)`?
  
• Question #9ed58
  
• How do you solve `2=4cos^2x+1` for `0<=x<=2pi`?
  
• How do you integrate by substitution `int x^3/sqrt(1+x^4) dx`?
  
• How do you integrate `int cos6x dx`?
  
• How do you integrate `int sin2x dx`?
  
• Question #6f533
  
• Question #312d6
  
• If `sum_(n=2) ^oo (1+k)^-n=2` what is `k`?
  
• Question #142c1
  
• Question #d9dbd
  
• Which number is equivalent to `3^4/3^2`??
  
• Question #452a0
  
• How do you find `\sum _ { n = 1} ^ { \infty } \frac { 15^ { n } } { ( n + 1) 6^ { 2n + 1} }`?
  
• How can you the least find denominator for 1/8 and 2/9?
  
• Question #0dedf
  
• Question #aec5e
  
• Using mathematical induction for integers n `>=` 1, prove a + (a+d) +...+ (a+nd) = 1/2 (n+1)(2a+nd)?
  
• Question #fc10d
  
• Question #b2380
  
• Question #0857c
  
• Question #e1ae5
  
• Among all pairs of numbers whose sum is 100, how do you find a pair whose product is as large as possible. (Hint: express the product as a function of x)?
  
• How do you solve `8^(2x-5)=5^(x+1)`?
  
• Question #afd88
  
• Question #34d52
  
• What is `\lim_{x \rightarrow 0} x^{2} \cos ( \frac{\pi}{x} )`?
  
• How do you find the limit of `sin((x-1)/(2+x^2))` as x approaches infinity?
  
• The `sqrt75` is between what two integers?
  
• If `2x- 5`, `x-1`, and `3x -8` are all integers and `x- 1` is the median of these integers, what is x?
  
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