Answers created by VNVDVI

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• How towrite out the first five terms of each geometric sequence here? (1) `a_1 = 2, r = 4` (2) `a_1 = 48, r = -1/3`
  
• How do you find `int sinx -1/csc(x)dx`?
  
• Is "betrayer" a word?
  
• How do you find the domain of `f(x) = (x-4)/(x+3)`?
  
• How do you find `lim 1+1/x` as `x->0^+`?
  
• What is `(pi)/12` radians in degrees?
  
• For `f(x)=x^-3`, `a=1`, and `2.5\lex\le3.5`, find the following?
  
• How do you integrate `(6x^5 -2x^4 + 3x^3 + x^2 - x-2)/x^3`?
  
• MacLaurin expansion from `f(x)=x^(t-m)\sin^2(4x)`?
  
• What is the domain of `f(x)= x/(x^2+1)`?
  
• Sin2x+cosx=0 solve the equation on the interval 0,2pi?
  
• Use series to evaluate the limit `\lim_(x\rarr0)(x^2/2-1-\cos(x))/x^4`?
  
• How do you evaluate the limit `sin(6x)/6` as x approaches `0`?
  
• Find the integral below?
  
• How do you use the direct comparison test to determine if `sume^(-n^2)` from `[0,oo)` is convergent or divergent?
  
• What is the antiderivative of `cos^2 x`?
  
• Integrate the following (below) using infinite `\bb\text(SERIES)`?
  
• How would you evaluate the following the indefinite integral? (use C for the constant integration)
  
• How do you rewrite this Logarithmic problem in expanded form?
  
• What is the improper integrals sqrtx ln 5x dx from 1 to e ?
  
• How to integrate 2x sec^2 x dx?
  
• The expression 1+cos2x/sin2x is equivalent to ?
  
• What is `lim_(x->-oo) x^2/(x^2-7)`?
  
• Set up expansion formula for Taylor Series `f(x)=\root(3)(x)` centered round `a=1`?
  
• The function `f:f(x)=-|x|+1` is decreasing in the interval...?
  
• How do you simplify `-(3)^-2`?
  
• Determine the values of `p` for which the integral below is convergent?
  
• How do you integrate `int 1/(x^2-x-20) dx` using partial fractions?
  
• Find the first four terms of the Taylor Series: `f(x)=xe^x` given `a=0`?
  
• What is the integral of `int sin^3xcos^2x dx` from `0` to `pi/2`?
  
• Set up Taylor expansion `\bb\color(red)\text(formula)` for `sqrt(x)` around `a=2`?
  
• Find the Taylor expansion `\color(red)\bb\text(formula)`... for `f(x)=1/x^2` given `a=4`?
  
• Integration of ; ((1/X(4 + Inx))dx?
  
• Is it possible to get some help? Thanks!
  
• How do you solve: sin2θ + cosθ = 0 between 0 and 2pi?
  
• Differentiate `(sqrt(x) + 1 )^2/ x` with respect to `X.`?
  
• Can a continuous function have asymptotes?
  
• What is the derivative of `f(x)=cos^-1(x)` ?
  
• How do you simplify `i^100`?
  
• How do you integrate `(cscx)^2`?
  
• If F (x)=x^2-1 then find f inverse?
  
• Find the arc length of the function `y=1/2(e^x+e^-x)` with parameters `0\lex\le2`?
  
• How do you test for convergence `(sin(2n))/(1+(2^n))` from n=1 to infinity?
  
• What is the Taylor series of f(z) = `1+z^2+1/(1+z^2)` ? Please save me! Thank you :)
  
• How do you simplify `5!`?
  
• Calculate the geometric series? Please
  
• Find the arc length of the function below?
  
• Dy/dx? Ln(sin^-1(x))
  
• Evaluate the definite integral.?
  
• Check for convergence or divergence in the following sequences?
  
• How do you show whether the improper integral `int ln(x)/x^3 dx` converges or diverges from 1 to infinity?
  
• Is the series indicated absolutely convergent, conditionally convergent, or divergent? `rarr\4-1+1/4-1/16+1/64...`
  
• How do you integrate `int cos(3t)cos(4t)dt`?
  
• Is the series `\sum_(n=1)^\infty\tan^-1(1/n)` absolutely convergent, conditionally convergent or divergent?
  
• `\sum_(n=2)^\infty ((x+2)^n)/(2^n\lnn)`?
  
• How do you find the value of `costheta` given `sintheta=-3/5` and in quadrant IV?
  
• How does one verify `(secx-cosx)^2=tan^2x-sin^2x`?
  
• How do you find a power series representation for `x^2 / ( 1 - 2x )^2`?
  
• How do you find the derivative of `y= sin(sin(sin(x)))` ?
  
• How do you solve this optimization question?
  
• How do you find the domain of `h(x)= 1/(x+1)`?
  
• How do you solve `2^(n+4)=1/32`?
  
• How do you prove that the function `f(x) = (x + 2x^3)^4` is continuous at a =-1?
  
• If `sqrt(x-1)=2`, what is `(x - 1)^2` ?
  
• A customer pumps $35.40 total in gas and pays with a $50 bill. What is the amount of change the customer should receive?
  
• How do you find the derivative of `f(x)= 1/x^2`?
  
• What is the derivative of `f(x) = ln(sinx))`?
  
• How do you use the fundamental theorem of calculus to find F'(x) given `F(x)=int (csc^2t)dt` from [0,x]?
  
• What is the solution to the equation `e^(5-3x)=10`?
  
• How do you simplify `4/(sqrt(4x) + sqrt(4x))`?
  
• The population of a town a town after t weeks is given by p(t)=1200(2^-t). a) what is the initial population of the town? b) how many people are there after 1 week? c) what is the rate of change of people after 1 week?
  
• Help Please! A radioactive substance decaying so that after t years, the amount remaining, expressed as a percent of the original amount is a(t) = 100(1.1)^-t. determine the function, a', which represents the rate of decay of the substance.?
  
• As above, a particle has velocity v(t)= `3t^2-2t-1` measured in m/s. Compute total distance traveled over [0,2] in meters?
  
• How do you find the integral of `xe^x - sec(7x)tan(7x) dx`?
  
• How do you find the 6-th partial sum of the infinite series `sum_(n=1)^oo1/n` ?
  
• This is a multiple choice question. A certain radioactive substance is decaying so that at time t, measured in years, the amount of the substance, in grams, is given by the function f(t)=-e^t +10. what is the rate of decay of the substance after 1 year?
  
• I don't know how this happen!!! Help me in fatorial?
  
• What is the radius of convergence of the MacLaurin series expansion for `f(x)= sinh x`?
  
• How do you differentiate `f(x)=sin(e^(3-x))` using the chain rule?
  
• How do you find `intx^2 e^(1-x)dx` using integration by parts?
  
• How do you find `intsqrtx lnxdx` using integration by parts?
  
• How do you find the value of `cot 0`?
  
• Express using a single log 3logab - 2logb - 3loga?
  
• Is the series `\sum_(n=1)^\infty((-5)^(2n))/(n^2 9^n)` absolutely convergent, conditionally convergent or divergent?
  
• Is the series `\sum_(n=1)^\inftyn^2/(n^3+1)` absolutely convergent, conditionally convergent or divergent?
  
• Is the series `\sum_(n=0)^\infty n^n/(4^n n!)` absolutely convergent, conditionally convergent or divergent?
  
• How do you integrate `int xe^(x/2)` using integration by parts?
  
• How do you find the integral of `(x^2)/(16-x^2)^(1/2)`?
  
• What is 1/2 to the negative fourth power?
  
• How do I find the derivative of `f(x) = sqrt(x+3)` using first principles?
  
• I don't understand this explanation for `\sum_(n=0)^\infty((-1)^n)/(5n-1)`? Why test for convergence/divergence AGAIN, if the Limit Comparison Test confirms that both series are the same?
  
• Integration of cos(logx)dx?
  
• Solve the equation for x : 2sinx+1=1 ?
  
• How do you simplify `(cos2x+sin^2x)/cos^2x`?
  
• Inverse of e to the power 2x?
  
• How do you find the integral of `int4x^3 sin(x^4) dx`?
  
• How do I find `sintheta` = `-cos^2theta` -1 in radians from `[0, 2pi]`?
  
• How do you solve `tan^2x/secx+cosx=2` for `0<=x<=2pi`?
  
• Evaluate `int ( 8(e^x -1))/(7x) dx` as a power series.?
  
• Are there any solutions for this equation within (0,2π)? [cosx=sinx] if so, what are they?
  
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