# Axel Alvarez

Calculus teacher | Experienced educator in USA

I hold a degree in Calculus from Tennessee Tech University, where I honed my passion for mathematical theory and application. With a commitment to excellence, I delve into the intricacies of calculus to demystify its principles for students. My journey at Tennessee Tech University equipped me with a deep understanding of mathematical concepts and effective teaching strategies. Through personalized guidance and clear explanations, I empower students to master calculus and excel in their academic pursuits. With dedication and expertise, I help learners navigate the complexities of calculus, fostering confidence and success in their mathematical journey.

## Questions

What is the limit of #(x^(6) + 4x^(4) - 8x^(2)) / [(x^(4) + 12x^(3) + 2x^(2) + 8)]^5# as x goes to infinity?

What is the Cartesian form of #(2,(pi)/4)#?

How do you find an equation of the tangent line to the curve at the given point #y=3arccos(x/2) # and #(1,pi)#?

How do you evaluate the definite integral #int 2^x dx# from #[-1,1]#?

How do you integrate #(-2x)/((x^2+2x+2)^2) #?

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

What is the MacLaurin Series for #sin(2x)ln(1+x)#?

What is the derivative of #cos(pi x)#?

How do you differentiate #-2y=x-cosy/(xy)#?

How do you evaluate the integral #int arctansqrtx#?

How do you use the Mean Value Theorem to solve #f(x)=x - sqrtx# on the closed interval [0,4]?

What is the general solution of the differential equation? : #y''+4y=2sin2x#

How do you find the derivative of #y=sin(tan2x)#?

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?

How do you find the derivative of #2^xln2#?

Is #f(x)=x^4-4x^3+x-4# concave or convex at #x=-1#?

What is the interval of convergence of #sum_1^oo xsin((pi*n)/2)/n #?

How do you find the radius of convergence #Sigma x^(3n)/5^n# from #n=[1,oo)#?

How do you differentiate #g(t)=(t-sqrtt)/(t^(1/3))#?

How do you differentiate #y = x * sqrt (4 - x^2)#?