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?