# 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

For #f(t)= (t^3-t+1,t^2-t)# what is the distance between #f(2)# and #f(5)#?

How do you differentiate #f(x)=(4x-3)/sqrt (2x^2+1) # using the quotient rule?

What is the derivative of #f(t) = (tsint , t^2-tcost ) #?

How do you find the volume of the solid generated by revolving the region bounded by the graph of #y = ln(x)#, the x-axis, the lines #x = 1# and #x = e#, about the y-axis?

How do I evaluate #int(csc^2x)/(cot^3x) dx#?

What is the derivative of #sin 5x#?

How do you differentiate #f(x)= ( x + 1 )/ ( xcot x )# using the quotient rule?

What is the indefinite integral of #sin (lnx) dx#?

How do you integrate #(6x^2 + 1) /( (x^2)(x-1)^3)# using partial fractions?

What is the maximum area of a rectangle that can be circumscribed about a given rectangle with length L and width W?

What is the net area between #f(x) = cos^2xsinx # and the x-axis over #x in [0, 3pi ]#?

What is the implicit derivative of #5=xy^3-3xy#?

How do you integrate #e^2xcosx dx#?

How to find (f) if f′(x)=16x^3+6x+7 and f(1)=−1 ?

How do you find #(dy)/(dx)# given #x^3-xy+y^3=1#?

How do you find the derivative of #g(t)=(10log_4t)/t#?

What is the arclength between two points on a curve? How does it differ from the distance?

How do you determine the limit of #(x+4)/(x-4)# as x approaches 4+?

What is the equation of the tangent line of #f(x)=1/(2x)+4 # at #x=2#?

What is the limit of #((x+1)/x)^x# as x approaches #oo#?