Comprehensive Multiplication Chart: Interactive and Printable Tables for Math Practice

Find the function represented by the following series and find the interval of convergence of the series. Sum of ((x - 5)^(2k))/(36^k) from k = 0 to infinity.

Alex Bettington

•August 23, 2024

$Find T(t) \enspace and \enspace N(t) for the curve r(t) = 4t^2 i + 6t j .$

Find T(t) \enspace and \enspace N(t) for the curve r(t) = 4t^2 i + 6t j .

Alex Bettington

•August 23, 2024

$Consider the curve r(t) = \langle e^{-5t}\cos(-1t), e^{-5t}\sin(-1t), e^{-5t} \rangle . Compute the arclength function s(t) (with initial point t=0 )$

Consider the curve r(t) = \langle e^{-5t}\cos(-1t), e^{-5t}\sin(-1t), e^{-5t} \rangle . Compute the arclength function s(t) (with initial point t=0 )

Alex Bettington

•August 23, 2024

Determine whether the vector field F(x,y) = (x+5) i +(6y+5) j is path independent (conservative) or not. If it is path independent, find a potential function for it.

Alex Bettington

•August 23, 2024

Let f(x) = 2x^2 - 2 and let g(x) = 5x + 1. Find the given value. f(g(-1)).

Alex Bettington

•August 23, 2024

Find the point(s) at which the function f(x) = 2 - x^2 equals its average value on the interval [-6,3] .

Alex Bettington

•August 23, 2024

Let f(x) = 7x^2 - 2 to find the following value. f(t + 1).

Alex Bettington

•August 23, 2024

$Find the average value of the function h(x) = 6\cos^4 x \sin x on the interval [0, \pi]$

Find the average value of the function h(x) = 6\cos^4 x \sin x on the interval [0, \pi]

Alex Bettington

•August 23, 2024

Find the arc length of the graph of the function over the indicated interval. (Round your answer to three decimal places.) y= 1/2(e^x+e^-x) and interval [0,2]

Alex Bettington

•August 23, 2024

Find the slope of the curve: x^3 - 3xy^2 + y^3 = 1 at the point (2, -1).

Alex Bettington

•August 23, 2024

$Determine the inverse Laplace transform of F(s) = \frac{3s+5}{s^2+4s+13}$

Determine the inverse Laplace transform of F(s) = \frac{3s+5}{s^2+4s+13}

Alex Bettington

•August 23, 2024

$Evaluate the integral \int \frac{1}{64x^2-9} \,dx$

Evaluate the integral \int \frac{1}{64x^2-9} \,dx

Alex Bettington

•August 23, 2024

$Let F = (6xyz + 2sinx, 3x^2z, 3x^2y). Find a function f so that F = \bigtriangledown f , and f(0, 0, 0) = 0 .$

Let F = (6xyz + 2sinx, 3x^2z, 3x^2y). Find a function f so that F = \bigtriangledown f , and f(0, 0, 0) = 0 .

Alex Bettington

•August 23, 2024

$Given the velocity function v = t^2 + \frac{4}{\sqrt[4]{t^3}} , find the acceleration and the position function.$

Given the velocity function v = t^2 + \frac{4}{\sqrt[4]{t^3}} , find the acceleration and the position function.

Alex Bettington

•August 23, 2024

A) Find the limit: limit as x approaches infinity of arctan(e^x). B) Evaluate the integral: integral from 0 to (sqrt 3)/5 of dx/(1 + 25x^2).

Alex Bettington

•August 23, 2024

$Find the curvature for r(t) = \langle 4\cos t, t, 4\sin t \rangle$

Find the curvature for r(t) = \langle 4\cos t, t, 4\sin t \rangle

Alex Bettington

•August 23, 2024

Find the average value of the function on the given interval. f(x) = x + 1; [0, 15]

Alex Bettington

•August 23, 2024

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below. If the perimeter of the window is 37 ft, express the area, A, as a function of the width, x, of the w...

Alex Bettington

•August 23, 2024