Answers edited by Andrea S.

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• Question #804a1
  
• How do you sketch the curve #y=x^3-3x^2-9x+5# by finding local maximum, minimum, inflection points, asymptotes, and intercepts?
  
• Find the roots of #z^5+1=0#?
  
• How do you test the improper integral #intx^2 dx# from #(-oo, oo)# and evaluate if possible?
  
• What is the equation of the line normal to # f(x)=sqrt(e^(sqrtx)# at # x=4#?
  
• Given #tantheta=-5/12# and #(3pi)/2<theta<2pi#, how do you find #tan(theta/2)#?
  
• What is the area below the curve #f(x)=x^3 -4x^2 +2x+ 8# and bounded by the y-axis, the x axis and x=3 expressed as an integral?
  
• Question #c9fff
  
• How do you integrate #1/(e^x(e^x+1))# using partial fractions?
  
• What is the domain and range of #y =arccos(sin(2x))#?
  
• How do you graph #y=(6x-1)/(3x-1)# using asymptotes, intercepts, end behavior?
  
• How to find the sum of the series #sum_"n=0"^oo(z^(4n)/((4n)!))# when |z| < 1 ?
  
• A minimum value of a sinusoidal Function is at #(pi/4, 3)#. The nearest maximum value to the right of this point is at #((7pi)/12, 7)#. What is the equation of this function?
  
• Two opposite sides of a parallelogram each have a length of #1 #. If one corner of the parallelogram has an angle of #(3 pi)/4 # and the parallelogram's area is # 4 #, how long are the other two sides?
  
• What is #f(x) = int 3x dx# if #f(2) = 7 #?
  
• How do you find the center and radius of the circle given #3x^2+3y^2+12x-6y+9=0#?
  
• How do you find intercepts, extrema, points of inflections, asymptotes and graph #y=xsqrt(16-x^2)#?
  
• How do you find the positive values of p for which #Sigma lnn/n^p# from #[2,oo)# converges?
  
• Please explain geometric and harmonic progressions?
  
• How do you use the limit comparison test to determine if #Sigma 1/(n(n^2+1))# from #[1,oo)# is convergent or divergent?
  
• How do you use the integral test to determine if #Sigma n^ke^-n# from #[1,oo)# where k is an integer is convergent or divergent?
  
• How do you find MacLaurin's Formula for #f(x)=sin(2x)# and use it to approximate #f(1/2)# within 0.01?
  
• How do you determine whether the graph of #f(x)=1/(5x)-x^19# is symmetric with respect to the origin?
  
• How do you use the first and second derivatives to sketch #y = x - ln |x|#?
  
• Question #7bf46
  
• Question #89694
  
• How do you use the epsilon delta definition to prove that the limit of #x/(6-x)=1# as #x->3#?
  
• How do you test the series #Sigma sqrt(n+1)-sqrtn# from n is #[0,oo)# for convergence?
  
• How do you integrate #int 1/(x^3 +4x) dx# using partial fractions?
  
• Question #dfe82
  
• What is the equation of the tangent line of #f(x)=3/(2x+4) # at #x=-1#?
  
• What are the local extrema of #f(x)= x^3-x+3/x#?
  
• How do you integrate #int xsqrt(3 + x^2)dx# using trigonometric substitution?
  
• How do you evaluate the integral #int dx/(2x-7)#?
  
• Question #50ca2
  
• What is the derivative of #-1/(sin(x)^2)#?
  
• What is the equation of the line tangent to # f(x)=1/(x^2-4) # at # x=-1 #?
  
• What is #f(x) = int xsqrt(3-x) dx# if #f(3) = 0 #?
  
• What is a solution to the differential equation #dy/dx=sqrt(xy)sinx#?
  
• How do you find #lim (10x^2+x+2)/(x^3-4x^2-1)# as #x->oo#?
  
• How do you evaluate the limit #(x^4-10)/(4x^3+x)# as x approaches #oo#?
  
• How do you determine whether the sequence #a_n=ln(ln(n))# converges, if so how do you find the limit?
  
• How do you find the radius of convergence #Sigma (1*4*7* * * (3n+1))/(n!)x^n# from #n=[0,oo)#?
  
• How do you evaluate the integral #int 1/(x^2-4)#?
  
• Determine whether the series # sum_(n=1)^oo (2n^2 +3n)/sqrt(5+n^5)# is convergent or divergent. How do i tell which comparison test to use?
  
• What are the points of inflection, if any, of #f(x)=2e^(-x^2) #?
  
• What are the critical points of #g(x)=x/3 + x^-2/3#?
  
• How do you find an equation of the tangent line to the curve #y=(2x)/(x+1)# at the point (1,1)?
  
• How do you show that the series #1+sqrt2+root3(3)+...+rootn(n)+...# diverges?
  
• How do you determine the convergence or divergence of #Sigma 1/ncosnpi# from #[1,oo)#?
  
• What is the domain of #f(x) = arcsin(1-x^2)#?
  
• What is the equation of the line normal to #f(x)=6x^3-8# at #x=7#?
  
• Question #2f21a
  
• Question #7bdf4
  
• Find the derivative using first principles? : #sin sqrt(x)#
  
• How do you find the local max and min for #x^5 ln x#?
  
• Question #ae7e8
  
• How do you prove that the integral of ln(sin(x)) on the interval [0, pi/2] is convergent?
  
• Which curve is this? Analytical geometry
  
• Sequence ?
  
• How do you factor #f(x)=x^3-12x^2+36x-32# completely, given that (x-2) is a factor?
  
• How do you use the sum or difference identities to find the exact value of #tan((23pi)/12)#?
  
• How do you use the Maclaurin series for #f(x) = ln abs((1+x)/(1-x))#?
  
• Question #36d91
  
• How do you find the derivative of #y=5+sinx#?
  
• How do you evaluate #\int \frac { 1} { x ^ { 2} + y ^ { 2} }#?
  
• How do you find the power series for #f'(x)# and #int f(t)dt# from [0,x] given the function #f(x)=Sigma 1/n^2x^(2n)# from #n=[1,oo)#?
  
• Question #bbb77
  
• How do you apply the ratio test to determine if #Sigma 1/(ln(lnn))^n# from #n=[3,oo)# is convergent to divergent?
  
• How do you find the limit of #sin(x^2−4)/(x−2) # as x approaches 2?
  
• Question #95baf
  
• How do you integrate #int xsin2x# by parts from #[0,pi]#?
  
• How do you simplify #sin 2x times sin7x#?
  
• How do you use the limit definition to find the derivative of #f(x)=(2-x)/(3x+1)#?
  
• How do you test the series #Sigma 1/(ln(n!))# from n is #[2,oo)# for convergence?
  
• A man repays a loan of $3250 by paying $20 in the first month and then increases the payment by $15 every month. How long will it take him to clear the loan?
  
• How do you integrate #int (root3x)#?
  
• What is the interval of convergence of #sum_1^oo [(2n)!x^n] / ((n^2)! )#?
  
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