John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

Learn To Find Derivative Of Tan(X) With Quotient Rule – Step-By-Step Guide

d/dx(tanx) sec²x To find the derivative of tan(x) with respect to x, we use the quotient rule. Let f(x) = sin(x) and g(x) = cos(x), then tan(x)...

John Rhodes
June 21, 2023
Algebra

The Axis Of Symmetry In Parabolas: Definition, Formulas, And Examples

axis of symmetry The line that divides a function into two matching halves In mathematics, the axis of symmetry (also known as line of symmetry) is an...

John Rhodes
June 21, 2023
Calculus

Calculating The Right Riemann Sum For Integrating A Function Over [1,7] With 3 Equal Intervals

Let f be the function given by f(x)=x2+1x√+x+5. It is known that f is increasing on the interval [1,7]. Let R3 be the value of the right...

John Rhodes
June 21, 2023
Calculus

Midpoint Riemann Sum: A Step-By-Step Guide To Approximating Integrals In Math

Let f be the function given by f(x)=x2e−x. It is known that ∫10f(x)ⅆx=0.160603. If a midpoint Riemann sum with two intervals of equal length is used to...

John Rhodes
June 21, 2023
Calculus

Find The Value Of X At Which G Attains A Relative Maximum Using The First Derivative Test In Calculus

Let g be the function defined by g(x)=∫x−1(−12+cos(t3+2t))ⅆt for 0

John Rhodes
June 21, 2023
Calculus

Calculating The Left Riemann Sum Of A Math Function With Four Subintervals.

The continuous function f is known to be increasing for all x. Selected values of f are given in the table above. Let L be the left...

John Rhodes
June 21, 2023
Calculus

Solving The Definite Integral Of Sin(X^3 + 2) Using The Fundamental Theorem Of Calculus

Which of the following limits is equal to ∫31sin(x3+2)ⅆx ? limn→∞∑k=1nsin((1+2kn)3+2)2n To solve this problem, we need to use the fundamental theorem of calculus, which states that...

John Rhodes
June 21, 2023
Calculus

Mastering Limits In Calculus: Transforming Sums Into Integrals And Evaluating A Limit

limn→∞∑k=1n(2+3kn−−−−−−√4⋅3n)= ∫2 to 5 4√xⅆx To find this limit, we can transform the sum into a definite integral using the limit definition of a Riemann sum. Specifically,...