# 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

What is the surface area of the solid created by revolving #f(x)=x^2# for #x in [1,2]# around the x-axis?

How do you evaluate the definite integral #int (-2x^2+3x+2)dx# from [0,2]?

Is #f(x)=(-7x^3-x^2-2x+2)/(x^2+3x)# increasing or decreasing at #x=1#?

How derivate this? Please help me

What is the derivative of this function #y=1/arcsin(2x)#?

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

How do you integrate #1/(1+tanx) dx#?

Is #f(x)=e^(2x)-x^2/(x-1)-1# concave or convex at #x=0#?

How do you use the epsilon delta definition to prove that the limit of #x^2-7x+3=-7# as #x->2#?

What are the critical values, if any, of #f(x)=x+e^(-3^x)#?

How do you use the limit definition to find the derivative of #2sqrtx-1/(2sqrtx)#?

How do you find the volume bounded by #y = 2x^(1/2)#, the line y = 2 and x = 4 revolved about y=2?

What is the instantaneous velocity of an object with position at time t equal to # f(t)= ((t-2)^2,5t-3) # at # t=2 #?

How do you integrate #intx cos 2x dx#?

How do you express as a partial fraction #1/(s^2 +1)^2#?

How do you find the derivative of #ln^2 x#?

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

What is the limit of #x# as x approaches #-4^-#?

How do you determine if rolles theorem can be applied to #f(x) = 2 − 20x + 2x^2# on the interval [4,6] and if so how do you find all the values of c in the interval for which f'(c)=0?

How do you find the first and second derivatives of #f(x)=(x)/(x^2+1)# using the quotient rule?