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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