# 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

Consider the function #f(x)=(10/x^2)-(7/x^6)# if f(1)=0, then what is f(x)?

How do you find the x coordinates of all points of inflection, final all discontinuities, and find the open intervals of concavity for #f(x)=2x^(5/3)-5x^(4/3)#?

How do you find the inflection points of the graph of the function: # f(x)= x^3 - 12x#?

How do you differentiate f(x) = x² ln(x) ?

A rectangular piece canvass with dimensions 10m by 6m is used to make a pool.Equal sizes squares are to be cut from each corner and remaining will folded up around some plastic tubing.what is the dimension of the pool so the water volume is maximum?

For #f(x)=(2x+1)^2/(x+1/2) # what is the equation of the tangent line at #x=-1#?

What is the largest interval on which the function is concave down for #f(x) = 5sin(x) + (sin(x))^2# over the interval #[-pi/3, 2pi/3]#?

What is the derivative of #y=3x^2e^(5x)# ?

How do you find the derivative of #(3x-(sin4x)^2)^(1/2)#?

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

How do you use the limit definition of the derivative to find the derivative of #f(x)=-4x^2-5x-2#?

How do you determine whether the sequence #a_n=sqrt(n^2+n)-n# converges, if so how do you find the limit?

How do you find the critical points for #y = x*sqrt(8-x^2)#?

How do you find the derivative of #y = (2x+3)^4 / x#?

How do you find the sum given #sum_(k=0)^4 1/(k^2+1)#?

How do you derive the formula for integration by parts?

What is the derivative of #x^(3/x)#?

How do you find the integral of #(e^(8x))sin(9x)dx#?

How do you find a power series representation for # (1+x)/((1-x)^2)#?

What is the antiderivative of # x/(x^2+1)#?