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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