# 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 find the volume of the solid formed by rotating the region enclosed by ?

What are the global and local extrema of #f(x)=2x^7-2x^5 # ?

How do you find the definite integral for: #sqrt(4+3(t^4))dt # for the intervals #[1, 4]#?

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 26 ft/s. At what rate is his distance from second base decreasing when he is halfway to first base?

Is the statement "if the limit of f(x) as x approaches c is 0, then there must exist a number k such that f(k)<0.001" a true or false statement?

How do you integrate #secx^4 dx#?

How do you find the definite integral of #(sqrt(2x+1))dx# from #[1, 4]#?

How do you prove that # int_0^1 \ x(1-x)^n \ dx = 1/((n+1)(n+2))# ?

How do you find dy/dx if #y = sin3x cos^(2)x#?

How do you differentiate #f(x) = tan(sinx) #?

How do you find the critical points for # y = x^3 + 12x^2 + 6x + 8 #?

How do you find the second derivative of #y=-5/(x+1)#?

What is the slope of the tangent line of #(1-x)(3-4y^2)-lny = C #, where C is an arbitrary constant, at #(1,1)#?

How do you find the limit of #(3x^2 - 5x + 1) / (4x^2 + 5x)# as x approaches infinity?

What is #int 1 / csc xdx#?

How do you take the derivative of #tan(x - y) = y/(1 + x^2) #?

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

Whats the derivative of #y=1/2 ln[(1+x)/(1-x)]#?

How do you find the average rate of change of #f(z) = 4 − 3z^2# from [-2,0]?

How do you determine dy/dx given #x^2+xy-y^3=xy^2#?