# 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 particular solution to #ysqrt(1-x^2)y'-x(1+y^2)=0# that satisfies y(0)=sqrt3?

How do you differentiate #y=cos(a^3+x^3)#?

What is the derivative of #y= e^(3x/4)#?

What is arc length parametrization?

How do you use implicit differentiation to find dy/dx given #sqrtx+sqrt(yx^2)=x#?

How do you differentiate #f(x) = (tan(x^2)) (sec sqrt(x))#?

How do you differentiate the following parametric equation: # x(t)=t, y(t)=t #?

What is the equation of the tangent line of #f(x)=sinx-x/cosx# at #x=pi/4#?

How do you use the second derivative test to find the local extrema for #f(x)=sin(x)#?

In the limit #lim_(t to oo) 1/(1+4t)=0# , how do you find #B>0# such that whenever #t>B#, #1/(1+4t)<0.01#?

What is the derivative of # (ln (x-4)) ^ 3#?

How do you find the limit of #sqrt(n^2+n) - (n)# as n approaches #oo#?

What is the integral of #int sin^3 (x)cos^3 (x) dx#?

What is the equation of the tangent line of #f(x) = (-x^2-x+3)/(2x-1)# at #x=1#?

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

What's the integral of #int sinx * tanxdx#?

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

How do you find the derivative of #sqrt(2x-1#)?

How do you use substitution to integrate #sec(v + pi/2) * tan(v + pi/2)#?

How do you find an equation to the tangent line to the curve #y = 2 sin^2x# at #x = Pi/4#?