# Isabella Ackerman

Calculus teacher | Verified Expert

With a passion for calculus ignited during my studies at Simmons University, I'm dedicated to unraveling the mysteries of mathematics for students. Armed with a deep understanding of the subject, I strive to make complex concepts accessible and enjoyable. From derivatives to integrals, I guide learners on a journey of mathematical discovery, fostering critical thinking and problem-solving skills along the way. Let's embark on this mathematical adventure together, where every question is an opportunity to explore the beauty of calculus.

## Questions

How do you find the value of c guaranteed by the mean value theorem for integrals #2sec^2x#?

What is #f(x) = int 1/(x-4) # if #f(2)=1 #?

What is the derivative of #f(x)=(cos^-1(x))/x# ?

How do I evaluate #int(13 x^2 + 12 x^-2)dx#?

How do you determine if the improper integral converges or diverges #int ln(sin(x))# from 0 to pi/2?

What is the net area between #f(x) = cosx # and the x-axis over #x in [0, 3pi ]#?

What is the slope of the line normal to the tangent line of #f(x) = sec^2x-sin^2x # at # x= (pi)/12 #?

What is the equation of the tangent line of #f(x)=e^(-x^2+x+pi)-sinx/e^x# at #x=pi/4#?

A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 2ft/s, how fast is the angle between the top of the ladder and the wall changing when the angle is #pi/4# rad?

What is the #n^(th)# derivative of #x^(-1/2) #?

How do I find the derivative of #y = (sin(e^x))^ln(x^2)#?

How do you find #lim 1/x^2-1/x# as #x->0#?

How do you find f'(x) using the limit definition given #f(x)=x^(-1/2)#?

How do you find the instantaneous rate of change for #h(t)=-5t^2+20t+1# for t=2?

For what values of x, if any, does #f(x) = sec((-15pi)/8+9x) # have vertical asymptotes?

How do you find the instantaneous rate of change of #y=4x^3+2x-3# at #x=2#?

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?

What is #lim_(x->oo) e^x/(x-1)# ?

What is the power series of #f(x)= ln(5-x)^2#? What is its radius of convergence?

How do you find the critical points for #x^2-5x+4# and state whether it is stable or unstable?