Answers created by Andrea S.

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• How do you use the ratio test to test the convergence of the series `∑k/(3+k^2)` from k=1 to infinity?
  
• How about solution?
  
• Does the value of a function at a point have to exist in order for the limit to exist at that point?
  
• Is sin(π/2*n^1/n) converges or diverges ???? Help asap , thanks
  
• How do you find the maclaurin series expansion of `f(x) = ln abs(1+x^5)`?
  
• What is `f(x) = int xe^x-x dx` if `f(-1) = 1`?
  
• How do you find the antiderivative of `int x^2/(4-x^2) dx`?
  
• What is the derivative of `ln(2x+1)`?
  
• How do you use the first and second derivatives to sketch `f(x) = sqrt(4 - x^2)`?
  
• What is the integral of cosine^6 (x) dx ?
  
• What is the derivative of `arcsec(x/2)`?
  
• Determine convergence or divergence for this series ? sin k/(k+1)!
  
• Is the statement "if limit of f(x)=L as x approaches c, then f(c)=L" a true or false statement?
  
• Find `lim_{x to oo} {pi/2 - arctan(x)}^(1/x)` ?
  
• How do you prove that the limit of `5x^2 =5` as x approaches 1 using the epsilon delta proof?
  
• How would you integrate `ln(x^2 + 1)`?
  
• How many critical points can a quadratic polynomial function have?
  
• Identify whether the infinite series converge absolutely conditionally or dont `sum_(n=1)^oo (-1)^(n+1) (n (arctan(n+1)-arctan (n))` (Apply Mean Value theorem to conclude)?
  
• How do you use the integral test to determine the convergence or divergence of `Sigma 1/sqrtn` from `[1,oo)`?
  
• `lim_(n->oo)prod_(k=2)^n(1-1/k^2)`?
  
• Put limit in big O little O notation?
  
• Lim (sin3t)/(sin2t) x-->0 how do we find it's limit?
  
• How do you find `a` for the derivative of `f(x)=x^2-ax` if the tangent has a y-intercept of -9 at the vertex?
  
• Solve in series `x^2`y''+xy'+(`x^2-k^2`)y=0?
  
• How do you find the derivative of `y=tan(x)` using first principle?
  
• Using the definition of convergence, how do you prove that the sequence `{5+(1/n)}` converges from n=1 to infinity?
  
• Help with a problem?
  
• How to show that `1/(2a) ln |(x - a)/(x + a)| + C` is equal to `1/(2a) ln |(x + a)/(x - a)| + K`?
  
• How do I evaluate `int\sqrt{20x^{2}-5}dx`?
  
• How can I solve this limit? lim x---->0 (sin^3x) /(x-sinx)^3
  
• How do you integrate `int x/sqrt(3x^2-6x+17) dx` using trigonometric substitution?
  
• Find `lim_{x to infinity} {pi/2 - arctan (x)}^1/x` ?
  
• How do you find a power series representation for `f(x)= x/(9+x^2)` and what is the radius of convergence?
  
• How do you integrate `1/(x^2+25)`?
  
• How to solve this using limit of sum? `int_0^1xe^xdx`
  
• What is the antiderivative of `ln x / x^(1/2)`?
  
• Why isn't `dy/dx = 3x + 2y` a linear differential equation?
  
• How do you integrate sec(x)^2(1+sin(x))?
  
• What is the interval of convergence of the Taylor series of `f(x)=cos(3x^2)`?
  
• How do you find a power series representation for `f(x)=ln(1+x)` and what is the radius of convergence?
  
• Let p be a +ve rational number if x^p is defined then lim x--infinity a/x^p = ???
  
• Given Y=sin(2sin^-1(x)), find dy/dx ?
  
• Solve the differential equation cos(x)dy/dx+y=sin(x) given that Y=2 when X=0 ?
  
• Lim x---->0 (1-cos3x)/(tan^2 3x) How can I solve this limit?
  
• If function `f` is differentiable at `c`, simplify `lim_(h->0)((f(c+h^2)-f(c))/h)`?
  
• How do you use the integral test to determine whether `int dx/lnx` converges or diverges from `[2,oo)`?
  
• What is the Taylor series expansion for the function f(x)=[1-cos(x)]/sin(x) ?
  
• What is the derivative of the function g(x)=ln(cosx) ?
  
• Tanx/sin2x? limit x->0
  
• Evaluate the taylor series sum: `sum_{n=2}^{∞} {(-1)^n 3^{n-1}(2n)}/(2^{2n-1})` ?
  
• How do you integrate `x^2/((x-3)^2(x+4))` using partial fractions?
  
• Is it possible to evaluate `sum_(n=1)^oosqrt(4n^2x^2-1)/(4n^2)` in terms of `x`?
  
• If y/x= arctan(x/y), then dy/dx= ?
  
• Find a general solution y (x) of non-homogeneous linear equations of the 2nd order with constant coefficients and special right side. How to solve? (pictures below) Thank you a lot!
  
• How do you find the limit of `ln x * tan^-1(x)` as x approaches infinity?
  
• How do you integrate `int 1/sqrt(x^2-16x-7)` using trigonometric substitution?
  
• Use the integral method to determine if the series converge or diverge:?
  
• Lim x->0 [log(1+ax)+log(1+bx)]/x =?
  
• Using the definition of convergence, how do you prove that the sequence `lim 1/(6n^2+1)=0` converges?
  
• How do you evaluate the definite integral `int e^(-x) dx` from `[0,2]`?
  
• How solve Derivatives of Trigonometric Functions?
  
• Differential: y = 1/tan x- 1/cot x ?
  
• What is the Antiderivative of (1-2x)/(x+1)?
  
• How do you find the maclaurin series expansion of `f(x) = e^(3x)`?
  
• How do you find the derivative of `(x-3) /( 2x+1)`?
  
• How do you integrate `int (2-x^2)/sqrt(x^2-4)dx` using trigonometric substitution?
  
• Integrate 2y^2/y^2+4?
  
• How to show that a triangle of maximum area inscribed in a given circle is an equilateral triangle?
  
• How to evaluate `int_1^2(e^(2x)/(e^x-1))` ? Can you solve it without substitution and somehow use chain rule?
  
• What is the limit as x approaches infinity of `e^(2x)cosx`?
  
• How do you find the integral of `[x^4(sinx) dx]`?
  
• Can we calculate integral of cos^4x as (cos^2x)^2 instead of cos^3x*cosx?
  
• Does this integral converge or do not converge? `int_(1/2)^2(1)/(x(lnx)^4)dx`
  
• Is the following series convergent?
  
• How do you integrate `int x^2/sqrt(16-x^2)` by trigonometric substitution?
  
• What is `f(x) = int 1/((x+3)(x^2+4) dx` if `f(2) = 0`?
  
• How do you determine the limit of `1/(x-2)^2` as x approaches 2?
  
• Differentiate the function with respect to x : e^x secX ?
  
• What is the derivative of `y= ln abs(secx-tanx)` for `x>0`?
  
• Sin(2sin^-1x)=?
  
• How do you evaluate the integral of `int sqrt (x^2 + 2x) dx`?
  
• What is `f(x) = int cotx-sec2x dx` if `f(pi/3)=-1`?
  
• What is the derivate of...?
  
• I need to find the derivative of a function for a given value of the argument Can smb help?
  
• How do you use the limit definition to find the derivative of `f(x)=(x+1)/(x-1)`?
  
• How can you find the antiderivative of 1/(1+3x²) ?
  
• What is the smallest parameter possible for a rectangle whose area is 16 square inches and what are it’s dimensions?
  
• How do you prove a limit of (x^2+3) as x approaches 1 equal 4? Thanks
  
• How do you integrate `int x/ (x^3-2x^2+x)` using partial fractions?
  
• What is the antiderivative of `x/(x^2 + 4)`?
  
• Is there a summation rule for continuous functions?
  
• How do you test the alternating series `Sigma (-1)^n/(ln(lnn))` from n is `[3,oo)` for convergence?
  
• How do you test the alternating series `Sigma (-1)^nsqrtn` from n is `[1,oo)` for convergence?
  
• How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given `1+3/4+9/16+...+(3/4)^n+...`?
  
• How to solve `int_(-pi/3)^(pi/3)` `(|x| + tan x)^2dx`?
  
• What is continuity at a point?
  
• How do you prove that the limit of `(2x^2 + 1) = 3` as x approaches 1 using the epsilon delta proof?
  
• Find the value of the taylor series sum: `sum_{n=4}^∞ \frac{(n+1)(n)2^n}{3^n}` ?
  
• Find the value of the power series sum: `sum_{n=2}^∞ \frac{(-1)^n}{(2n+1)(2n+2)3^n}` ?
  
• Would like to solve this integral but it kind of messy especially when it comes to end?
  
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