Answers created by Andrea S.

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• How do you find the intervals of increasing and decreasing using the first derivative given #y=(x+2)^2(x-1)#?
  
• Find #\int_0^ooe^(-ax)\sin(bx)dx#?
  
• What is #int_(1)^(oo) 1/x-1/(x-1) dx #?
  
• Solving this linear D.E. using an integrating factor?
  
• Solve the differential equation : dy/dx +y/x =x²y^6 ?
  
• What is the improper integral (arctan2x)/(pi(1+4x^2)) dx from 0 to infinity ?
  
• How do you integrate #int 1/sqrt(4x^2+12x-5) # using trigonometric substitution?
  
• How do you find#int x^3/sqrt(2x^2 + 4) dx # using trigonometric substitution?
  
• How do you find an expression for #sin(x)# in terms of #e^(ix)# and #e^(ix)#?
  
• How do you find the limit of #(3x^2-x-10)/(x^2+5x-14)# as x approaches 2?
  
• Range of a function f(x)=cos(k sin x)is [-1,1] then the least positive integral value of k will be?
  
• How do you integrate # (2x-5)^2 dx#?
  
• Integration in square root of 1+cosx ÷ 1-cosx?
  
• INTEGRATION sin(lnx)dx?
  
• Find #f# and 'calculate' the integral?
  
• Is it possible to solve this integral by hand or by conventional methods?
  
• How is integration by substitution related to the chain rule?
  
• How do you find the Taylor polynomial of degree 10 of the function #arctan(x^3)# at a = 0?
  
• How do you use Part 1 of the fundamental theorem of calculus to find the derivative of the function #y= int (1+v^2)^10 dv# from sinx to cosx? Please help have been looking at problem for a hour can't figure out how to work it?
  
• INTEGRATION 1/sqrt8x-x^2 dx?
  
• PLEASE HELP: Some equations which do not appear to be separable can be made so by means of a suitable substitution. By means of the substitution z=y⁄x solve the following equation: dy/dx=y^2/x^2 +y/x+1. ??
  
• Find power series expansion and give its interval of validity for #int_0^x t^(-1)ln(1+2t)dt# ?
  
• How do you find the derivative of #x(x-4)^3#?
  
• How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(x+3)# ?
  
• How do you find #\int \frac { 2x + 5} { x ^ { 3} + 6x ^ { 2} + 9x } d y#?
  
• Compute ∫y*(y^4+y^2+4)^(1/2)dy ?
  
• How do you integrate #int sinx*e^-x# by integration by parts method?
  
• Find the dimensions of the rectangle of maximum area whose perimeter is 16 cm ?
  
• How do we solve an integral using trigonometric substitution?
  
• How do you maximize the perimeter of a rectangle inside a circle with equation: #x^2+y^2=1#?
  
• How do you use the quotient rule to differentiate #3/(3x+3)#?
  
• For a continuous function #f#, is it generally true that #\int_0^2 f(x)dx = \int_0^1 f(2x)dx#?
  
• How to find the derivative of (cosec^2x) ?
  
• Question: Find the particular solution #y_p(x)# of homogeneous linear equation of the 2. order with constant coefficients. How do I solve it? Thank you! (pictures below)
  
• How do you use the limit comparison test on the series #sum_(n=1)^oo(n+1)/(n*sqrt(n))# ?
  
• Please help with this differentiation question?
  
• What is the antiderivative of #x sin (x/2)#?
  
• How do you solve this partial fraction? 2x^2-x+4/x^3+4x
  
• How do you find the integral of # (sinx)(5^x) dx#?
  
• Hi everyone! My question is: "find the general solution y(x) of the given differential equation": #xy'+y=x^6# How do I solve this? Thank you for your answer!
  
• Using integrals, find the area of the circle #x^2 + y^2 = 1# ?
  
• How do you integrate #int 1/sqrt(9x^2-6x-3) # using trigonometric substitution?
  
• Find the derivative of f(x)= x^3/2 using the limit definition ?
  
• Find the exact length of the curve (parametrics)?
  
• Prove using the #epsilon-delta# method that #lim_(n->oo) (2n^2+1)/(7n^2+n+5) = 2/7# ?
  
• How do you use the limit comparison test to determine if #Sigma (n+3)/(n(n+2))# from #[1,oo)# is convergent or divergent?
  
• Using the limit definition, how do you differentiate #f(x)=(x+1)^(1/2)#?
  
• How do you integrate #int 1/sqrt(9x^2-6x+5) # using trigonometric substitution?
  
• How can I calculate #int_-1^0(x^2*sqrt(1+x^3))dx# ?
  
• Using the limit definition, how do you find the derivative of # f(x) = 4 -2x -x^2#?
  
• How do you integrate #int (x^2)/(x^2 + 3x -4) dx# using partial fractions?
  
• How do you differentiate #x / (x^2 + 1)^(1/2)#?
  
• What is the derivative of #f(x)=ln(x/sinx)#?
  
• Does the sequence converge or diverge? #lim sin(4n)/(7+sqrtn)#?
  
• Find out a function (fx) so that as x gets closer to 1, value of f(x) gets bigger?
  
• Integrate x-1/(x+1)²?
  
• Integrate the following using INFINITE SERIES (no binomial please)?
  
• What is the integration of 1/(1-sec(θ)) dθ?
  
• Fundamental theorem of calculus: Local max of f(t)?
  
• Find (and prove) a general formula for integration of a^(bx) cos(cx) dx for any constants a, b, c?
  
• How do you evaluate the indefinite in integral? Use C for constant integration
  
• Let f(x) = 1/x and find the equation of the tangent line to f(x) at a "nice" point near 0.203, how do you use this to approximate 1/0.203?
  
• How do you know if the series #sum 1/(n^(1+1/n))# converges or diverges for (n=1 , ∞) ?
  
• What makes a function continuous at a point?
  
• How do you find #\int ( 4- 3\cos x ) ^ { \frac { 1} { 2} } d x#?
  
• How do you evaluate the integral of #int (2 -1/x)dx# from 1/2 to 3?
  
• Integrate the following using infinite #\bb\text(series)# ?
  
• If #a_n# converges and #lim_(n->oo) a_n -b_n=c#, where c is a constant, does #b_n# converge?
  
• How to find the coefficient of any term in the power series expansion?
  
• What is the probability of rolling two even numbers in one roll of a pair of dice?
  
• From a normal pack of 52 playing cards, one card is selected at random. How can I find the probability of the card being either a black card or an ace?
  
• How is the infinite series from n=0 to infinity of 3(2^(n+1))/5^n=10?
  
• Express the integrand as a sum of partial fractions and evaluate the integral. Integral (6x^2+2x+7)/(x^3-1)?
  
• 𝐼𝑓 𝑦=𝑠𝑒𝑐^2 𝑥⁡ 𝑐𝑠𝑐^2 𝑥 ,𝑡ℎ𝑒𝑛: 𝑑𝑦/𝑑𝑥= …?
  
• How do you find the integral of #int 1/(1 + sec(x))#?
  
• Use the derivative (below) to find the integral of #cos^nx dx#?
  
• What is the derivative of # tan(x-y)=y/(1+x^2)#?
  
• How do you find the definite integral of #(dx)/(xsqrt(ln(x))# from #[e^4, e^16]#?
  
• What is #f(x) = int (x+1)/((x+5)(x-4) ) dx# if #f(2)=1 #?
  
• What is the derivative of this function #e ^ sin (2x)#?
  
• How do we show that this is true?
  
• How to do this question?
  
• Evaluate dy/DX=2y²/x³?
  
• (dy/dx)-y=4y^5?
  
• How do you find the derivative of #y=x^(ln(x))#?
  
• How do you use the epsilon delta definition to find the limit of #x^3# as x approaches #0#?
  
• How do you find the extrema for #g(x) = sqrt(x^2 + 2x + 5)#?
  
• How do you integrate #int x+cosx# from [pi/3, pi/2]?
  
• What are the global and local extrema of #f(x)=x^2 -2x +3# ?
  
• How do you differentiate #f(x)=e^(x^2+x+8) # using the chain rule?
  
• How do you find the antiderivative?
  
• How do you integrate #int e^xcosx# by integration by parts method?
  
• How do you find the maclaurin series expansion of #1/(x+3)#?
  
• How do we find the radius of convergence?
  
• How to find radius of convergence for the taylor series of #(sinx)^2#?
  
• How do you use the formal definition of a limit to find #lim 4x -1# as x approaches 2?
  
• For question a, why do we use cos, where does it come from?
  
• What is the integral of #int sin^(4) (2x) dx#?
  
• The point on the parabola y=(x-3)^2 that is near to the origin?
  
• How do you find the integral of #(2dx) /(x^3sqrt(x^2 - 1))#?
  
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