# Aurora Alvarado

Calculus teacher | Tutor for 9 years

I am a passionate educator specializing in Calculus. With a degree from Drew University, I bring a deep understanding of mathematical concepts to my teaching. My goal is to make complex topics accessible and engaging for students, fostering a love for learning and problem-solving. I believe in creating a supportive and inclusive learning environment where students feel empowered to ask questions and explore new ideas. Whether it's derivatives or integrals, I'm here to guide students through the world of Calculus with patience and enthusiasm. Let's embark on this mathematical journey together!

## Questions

How do you find the exact relative maximum and minimum of the polynomial function of #2x^3 -23x^2+78x-72#?

Is there a difference between #lim_(h->0)(f(x+h)-f(x))/h# and #lim_(deltax->0)(f(x+deltax)-f(x))/(deltax)#?

How do you differentiate #f(x)=(sinx+1)(x^2-3e^x)# using the product rule?

How do you find the integral of #int (1 + cos x)^2 dx#?

How do you show that the curve #6x^3+5x-3# has no tangent line with slope 4?

How do you implicitly differentiate #4= xytan(x^2y) #?

What is the vertical asymptote of ln(x)?

How do you integrate #int (lnx)^5/x# using substitution?

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

What is the derivative of #tan^4 (x)#?

What is the derivative of #arctan(x^2+1)#?

How do you integrate #int sin^-1x# by integration by parts method?

The region under the curves #x, y>=0, y=x^2sqrt(1-x^4)# is rotated about a) the x axis and b) the y axis. How do you sketch the region and find the volumes of the two solids of revolution?

How do you find the instantaneous rate of change of the function #y= 5x - x^2# when x=-2?

Given the function #f(x)=abs(x-3)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,6] and find the c?

How do I find the derivative of #ln sqrt(x^2-4)#?

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

How do you find points of inflection and determine the intervals of concavity given #y=xe^(1/x)#?

How do I evaluate the indefinite integral #intsec^2(x)*tan(x)dx# ?

How can I solve the mentioned problem?Please,help.