# Luke Alvarez

Calculus teacher | Tutor for 6 years

I hold a degree in Calculus from the Fashion Institute of Technology. My passion lies in deciphering the intricate language of numbers and functions. Through personalized tutoring sessions, I strive to demystify calculus concepts, making them accessible and engaging for students. With a deep understanding of mathematical principles and real-world applications, I empower learners to conquer challenges and unlock their full potential. Whether it's derivatives, integrals, or differential equations, I am committed to fostering a supportive learning environment where curiosity thrives and mathematical fluency flourishes. Join me on a journey of discovery and mastery in the world of calculus.

## Questions

How do you integrate #int ( x^2 + 7x +3) /( x^2 (x + 3))# using partial fractions?

How do you use a graph to show that the limit does not exist?

What is the derivative of #1/(1+x^4)#?

What is #int tan(2x-3)*cot(3x) #?

How do you use the definition of a derivative to find f' given #f(x)=sqrtx# at x=1?

What is the antiderivative of #1/cosx(2+sinx)#?

How do you differentiate #f(x)= ( 2 - xsecx )/ (x -3) # using the quotient rule?

How do you find the Maclaurin Series for # (sin(x/11))^2#?

How do you evaluate the definite integral #int sqrtx(1-x)dx# from [0,1]?

What is the arc length of the curve given by #f(x)=xe^(-x)# in the interval #x in [0,ln7]#?

How do you use implicit differentiation to find #(dy)/(dx)# given #x^2+xy+y^2=9#?

What is the implicit derivative of #25=sin(xy)/x-3xy#?

How do you integrate #int6x ln x dx# from 2 to 4?

What is # I = int \ sinlnx-coslnx \ dx #?

How do you use differentials and the function #f(x,y) = arctan(x*y^2)# to approximate the value of f(0.94, 1.17)?

Given that # sin(x/y) = 1/2 # find #dy/dx#?

How do you integrate #x^15 dx#?

How do you find the volume of the solid obtained by rotating the region bounded by y=5x^2 ,x=1 , and y=0, about the x-axis?

How do you find the limit of #(x^2-9)/(x^2+2x-3)# as x approaches 3?

How do you find the average rate of change of #f(x)=10x^3+10# over the interval [1,3]?