# 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 I evaluate #int(13 x^2 + 12 x^-2)dx#?

What is #int sin x/ ( 1-cos^2x)dx#?

What is the inverse function of #f(x)=1/(1+x)#. How inverse functions appear in graph?

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

How do you evaluate the integral of #int x/[(x^2)+1]dx#?

How do you find the slope of the secant lines of #f(x) = sqrtx# at P(4,2)?

Given #f(x)= x^3 +2x -1#, how do you find #1/ [f^(-1)(2)]#?

What are the points of inflection, if any, of #f(x) = -3x^4-2 x^3 +9 #?

The point on the parabola y=(x-3)^2 that is near to the origin?

How do you use the limit definition to find the slope of the tangent line to the graph #f(x)= 1/(x+2)# at (0,1/2)?

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

How do you implicitly differentiate # y^2+(y-x)^2-y/x^2-3y#?

How do you find the derivative of y in the equation #ln(xy)=x+y#?

How do you differentiate # f(x) = tan^2(3/x) #?

How do you use the Ratio Test on the series #sum_(n=1)^oo9^n/n# ?

How do you find the general solution to #dy/dx=1/sec^2y#?

I tried a lot to solve this question, and every time i get 2, while the correct answer is 4, HELP to solve it?

What is #lim_(x->oo) e^x/(x-1)# ?

What is #lim_ (xrarr0) (1/x -1/x^2-x)#?

How do you find the average rate of change of #f(t) = 1.1t^2 - 2.5t + 1.5# over the interval [3,5]?