# 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 differentiate #f(x)=ln(sinx)/cosx# using the quotient rule?

If #y = 1/(1+x^2)#, what are the points of inflection of the graph f (x)?

What are the first two derivatives of #1/ln(x)#?

How do you solve this optimization question?

How do you find the integral #ln x / x#?

What is the antiderivative of #sinx#?

How do you find the derivative of the function: #arctan (cos x)#?

What is the derivative of #sin (x/2)#?

What is the slope of the tangent line of #r=theta/3+sin((3theta)/8-(5pi)/3)# at #theta=(7pi)/6#?

How do you integrate #(2x^2+4x+12)/(x^2+7x+10)# using partial fractions?

Let #f_n(x) = sum_(r=1)^n \ sin^2(x)/(cos^2(x/2)-cos^2(( (2r+1)x)/2) ) # and #g_n(x) = prod_(k=1)^n f_k(x) #. If #I_n=int_0^pi (f_n(x))/(g_n(x)) dx # show that #sum_(k=1)^n I_k = Kpi#, and find #K#?

How do you compare either points (0,0) and (-1,-1) to see if it is max min or point of inflection for #y= 36x^2 +24x^2#?

How do you differentiate #f(x)=e^(x^2)/(e^x-x^2)# using the quotient rule?

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

How do you find the x and y coordinates of all inflection points #f(x) = x^4 - 12x^2#?

How do you find the derivative of #(3x+1)^(3/2) (2x+4)#?

How do you differentiate #y=(sinx)^lnx#?

How do you integrate #int (x^2+2x)/(x^2+2x+1)# using substitution?

For what values of x, if any, does #f(x) = 1/(x^2-4x+4) # have vertical asymptotes?

How do you evaluate the integral #(1+tan(x))^3 * sec^2(x)dx# within the range [0,pi/4]?