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 differentiate # arctan(8^x)#?
How do you integrate #int e^(2x)cosx# by integration by parts method?
How do you evaluate the limit #root4(2cosx-5)# as x approaches 0?
How do you find the slope of the secant lines of # f (x) = x^2 − x − 42# at (−5, −12), and (7, 0)?
What will be the expansion of #sqrt(x+h)# in powers of #x and h#?
How do you determine if #a_n=1+3/7+9/49+...+(3/7)^n+...# converge and find the sums when they exist?
How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)(2n+1))+...#?
How do you find the slope of the secant lines of #f(x) = 2/x + 2# through the points: (0, f(0)) and (0+h, f(0+h))?
How do you find the integral of #(1/(e^x+e^-x))dx#?
How do you integrate #int 3/(xsqrt(x^2-9))# by trigonometric substitution?
How do you differentiate #x^4+4x^3y+y^4=1#?
How do you find the slope of the polar curve #r=cos(2theta)# at #theta=pi/2# ?
How do you find #(dy)/(dx)# given #4x=-5y^2-x^2y+4#?
How do you find the derivative of #y=1+x^-1+x^-2+x^-3#?
Use Newton's method to approximate the indicated root of the equation correct to six decimal places? The root of #f(x) =x^4 − 2x^3 + 3x^2 − 6 = 0# in the interval [1, 2]
What is the equation of the normal line of #f(x)= -2x^3-10x # at #x=2 #?
What is the derivative of #f(x)=e^(4x)*ln(1-x)# ?
What is the equation of the tangent line of #f(x) =(x^2)/(x-4)# at #x=5#?
Does #a_n=x^n/(n!) # converge for any x?
How do you integrate #int (x^2+1)sqrt(x-2)# using substitution?