# 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 horizontal asymptote of a curve?

Prove that the arc length of the polar curve #r = a(1-cos theta)# is #8a#?

What is # lim_(x rarr 0) (h(3+x)-h(3) )#?

How do you evaluate the limit #(3x^4-x^2+5)/(10-2x^4)# as x approaches #oo#?

Evaluate the limit? : # lim_(x rarr oo)(3x+1)/(|x|+2) #

How do you find the indefinite integral of #int (4sinx)/(3tanx)dx#?

How do you find the derivative of #(x-3) /( 2x+1)#?

Derivative: find a slope of tangent line=square root of 4-5x when x=-1 ?

What is #f(x) = int (3-x)e^x dx# if #f(0)=-2 #?

How do you find the derivative of # csc^-1 (u)#?

How do you use the chain rule to differentiate #y=7/(2x+7)^2#?

What is the derivative of #xsqrt(1-x)#?

Is there a difference between #lim_(h->0)(f(x+h)-f(x))/h# and #lim_(deltax->0)(f(x+deltax)-f(x))/(deltax)#?

How do you find the equation of the tangent line to the curve #y=1+x^3# that is parallel to the line #12x-y=1#?

What is the derivative of # ln(x^2+y^2)#?

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

How do you find the integral of #int (1 + cos x)^2 dx#?

How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y=x^(1/2)#, #y=0#, and #x=4# rotated about the x axis?

Let #y = f(x)# be a twice-differentiable function such that #f(1) = 2# and . What is the value of #(d^2y)/(dx^2)# at # x = 1#?

A point is moving along the curve #y=sqrt(x)# in such a way that its x coordinate id increasing at the rate of 2 units per minute. At what rate is its slope changing (a) when x=1? (b) when x=4?