# Christopher Agresta

Calculus teacher | Verified Expert

I specialize in Calculus, holding a degree from Scripps College. With a passion for mathematics and a knack for simplifying complex concepts, I guide students through the intricacies of calculus with clarity and enthusiasm. My approach emphasizes problem-solving skills and fosters a deep understanding of mathematical principles. Let's tackle calculus together and unlock its beauty and power.

## Questions

A street light is at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 ft from the base of the pole?

How do you differentiate #sinx+xy+y^5=pi#?

A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?

How do you use substitution to integrate # (2x+3)/(x+7)^3 #?

For #f(x) =(x-3)/(x-4)#, what is the equation of the line tangent to #x =3#?

How do you find the discontinuity of a function?

How do you use implicit differentiation to find dy/dx given #xy^2+x^2y=x#?

How do you use the chain rule to differentiate #y=(x^2+3x)^(-1/2)#?

Evaluate the integral #int \ sinx/(2+cos^2x) \ dx #?

How do you integrate #int 1/(x^2sqrt(x^2-7))# by trigonometric substitution?

How do you find a power series representation for # (1+x)/((1-x)^2)#?

If #f(x) =tan^2x # and #g(x) = sqrt(5x-1 #, what is #f'(g(x)) #?

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

How do you find a power series representation for #e^(-x^2)# and what is the radius of convergence?

What is the derivative of #sin^2 x + cos^2 x#?

How do you find #lim (5x+6)/(x^2-4)# as #x->oo#?

What is the antiderivative of #f(x) = 5#?

What is the equation of the line normal to # f(x)=-sqrt((x+1)(x+3)# at #x=0#?

What is the antiderivative of # 1/(xlnx)#?

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