Answers edited by Wataru

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• How do you use Power Series to solve the differential equation `y''=y` ?
  
• How do you use the direct comparison test for infinite series?
  
• How do you sketch the curve `f(x)=e^x/(1+e^x)` ?
  
• How do you find the limit as x approaches 2 of the piecewise function `f(x)={(4-x^2,if x<=2),(x-1,if x>2):}` ?
  
• What is the formal definition of limit?
  
• How do you use Power Series to solve the differential equation `y'=xy` ?
  
• How do you find the slope of the polar curve `r=3sec(2theta)` at `theta=pi/6` ?
  
• How do I use the Mean Value Theorem to so `4x^5+x^3+2x+1=0` has exactly one real root?
  
• How do you find the differentiable points for a graph?
  
• How do you find the equation of the tangent lines to the polar curve `r=sin(2theta)` at `theta=2pi` ?
  
• How do you use a power series to find the exact value of the sum of the series `1-(pi/4)^2/(2!)+(pi/4)^4/(4!) -(pi/4)^6/(6!) + …` ?
  
• How do you find the power series representation of a function?
  
• How do you evaluate the integral `int_0^1x^2dx` ?
  
• How do you use the Integral test on the infinite series `sum_(n=1)^oo1/(2n+1)^3` ?
  
• How do I find the partial fraction decomposition of `(t^4+t^2+1)/((t^2+1)(t^2+4)^2)` ?
  
• What is the Mean Value Theorem for continuous functions?
  
• How do you find the Slope of the curve `y=sqrt(x)` at the point where `x=4`?
  
• How do you find the parametric equations for a line segment?
  
• What is the Alternating Series Test of convergence?
  
• How do I use the limit definition of derivative to find `f'(x)` for `f(x)=c` ?
  
• What does exponential decay mean?
  
• How do you find limits on a graphing calculator?
  
• How do you find the derivative of `y=f(x)+g(x)`?
  
• What does exponential growth mean in biology?
  
• How do you find the horizontal asymptote of the graph of y=3x^6-7x+10/8x^5+9x+10?
  
• How do you find the product of power series?
  
• How do you Use the trapezoidal rule with four equal subdivisions to approximate a definite integral?
  
• How do you find the volume of the solid with base region bounded by the curve `9x^2+4y^2=36` if cross sections perpendicular to the `x`-axis are isosceles right triangles with hypotenuse on the base?
  
• How do you find the displacement of a particle that moves along a line?
  
• What are separable differential equations?
  
• How do you find the derivative of `y =sqrt(2)`?
  
• How do you find the points on the ellipse `4x^2+y^2=4` that are farthest from the point `(1,0)`?
  
• How do you find all intervals where the function `f(x)=1/3x^3+3/2x^2+2` is increasing?
  
• Find the limit as x approaches infinity of `x^7/(7x)`?
  
• How do you find the Maclaurin series of `f(x)=ln(1+x)` ?
  
• How I do I prove the Chain Rule for derivatives?
  
• How do you use Power Series to solve the differential equation `y''+y=0` ?
  
• How do you know when to use the first derivative test and the second derivative test?
  
• How do you evaluate the integral `int3e^(x)-5e^(2x) dx`?
  
• What is the derivative of `f(x)=cot^-1(x)` ?
  
• How do you find two numbers whose difference is 100 and whose product is a maximum?
  
• What are some examples of functions with asymptotes?
  
• How do you find the volume of the solid with base region bounded by the curve `y=e^x`, `y=ln4`, and the `y`-axis if cross sections perpendicular to the `y`-axis are squares?
  
• How do you test a power series for convergence?
  
• How do you use the Nth term test on the infinite series `sum_(n=1)^ooarctan(n)` ?
  
• How does Leibniz notation work for second derivatives?
  
• How do I find the partial fraction decomposition of `(x^4)/(x^4-1)` ?
  
• What is the opposite of exponential decay?
  
• How do you find the volume of a solid of revolution using the disk method?
  
• What is interval of convergence for a Power Series?
  
• What is asymptotic Discontinuity?
  
• How do you use the limit comparison test on the series `sum_(n=1)^oon/(2n^3+1)` ?
  
• How do you find the Maclaurin series of `f(x)=sin(x)` ?
  
• How do you find one sided limits algebraically?
  
• How can an infinite series have a finite sum?
  
• What is the interval of convergence of the series `sum_(n=0)^oo((-3)^n*x^n)/sqrt(n+1)`?
  
• How do you Find the exponential growth factor?
  
• What is the limit of `(2x-1)/(4x^2-1)` as `x` approaches `-1/2`?
  
• How do you find the derivative of `y=e^x`?
  
• Question #db99f
  
• How do I use the limit definition of derivative to find `f'(x)` for `f(x)=5x-9x^2` ?
  
• Can points of inflection be extrema?
  
• How do you use a power series to find the exact value of the sum of the series `1-pi^2/(2!)+pi^4/(4!) +pi^6/(6!) + …` ?
  
• Question #babaa
  
• How do you find the area of the region bounded by the polar curves `r=cos(2theta)` and `r=sin(2theta)` ?
  
• How do you use a graph to show that the limit does not exist?
  
• What is the vertex of `f(x)=x^2+4x+3`?
  
• How do you change rectangular coordinates to polar coordinates?
  
• How do you use the binomial theorem to find the Maclaurin series for the function `y=f(x)` ?
  
• How do you find a vertical asymptote for y = sec(x)?
  
• How do you solve separable first-order differential equations?
  
• How do you find the area of the region bounded by the polar curves `r=sqrt(3)cos(theta)` and `r=sin(theta)` ?
  
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