Comprehensive Multiplication Chart: Interactive and Printable Tables for Math Practice

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

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

Alex Bettington

•August 23, 2024

$Find velocity and position that has the acceleration a(t)= \langle 3e^t, 18t,2e^{-t} \rangle and specified velocity and position conditions: v(0)=(3,0,-6) \enspace and \enspace r(0)=(6,-1,2)$

Find velocity and position that has the acceleration a(t)= \langle 3e^t, 18t,2e^{-t} \rangle and specified velocity and position conditions: v(0)=(3,0,-6) \enspace and \enspace r(0)=(6,-1,2)

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

$Evaluate the integral \int \frac{\log x}{x} \, dx$

Evaluate the integral \int \frac{\log x}{x} \, dx

Alex Bettington

•August 23, 2024

Let F = (7yz)i + (6xz)j + (6xy)k. Compute the following: A) div F B) curl F C) div curl F (Your answers should be expressions of x, y, and/or z)

Alex Bettington

•August 23, 2024

$Evaluate the Integral \int \tan^2 x \sec^3 x \, dx$

Evaluate the Integral \int \tan^2 x \sec^3 x \, dx

Alex Bettington

•August 23, 2024

$Given f'(x)=\frac{\cos(x)}{x} and f(4)=3 , find f(x)$

Given f'(x)=\frac{\cos(x)}{x} and f(4)=3 , find f(x)

Alex Bettington

•August 23, 2024

$Evaluate the integral \int_1^4 3\sqrt t \ln(t) \, dt$

Evaluate the integral \int_1^4 3\sqrt t \ln(t) \, dt

Alex Bettington

•August 23, 2024

Find an equation of the tangent line to the curve y = x^3-3x+1 at the point (1,-1)

Alex Bettington

•August 23, 2024

$Consider the vector \mathbf F(x,y,z) = (2x+4y)\mathbf i +(4z+4x) \mathbf j + (4y + 2x) \mathbf k . a. Find a function f such that \mathbf F = \nabla f and f(0,0,0) = 0 . b. Suppose C is...$

Consider the vector \mathbf F(x,y,z) = (2x+4y)\mathbf i +(4z+4x) \mathbf j + (4y + 2x) \mathbf k . a. Find a function f such that \mathbf F = \nabla f and f(0,0,0) = 0 . b. Suppose C is...

Alex Bettington

•August 23, 2024

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

Alex Bettington

•August 23, 2024

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

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

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

Alex Bettington

•August 23, 2024

Find curl F(x,y,z) , when F(x,y,z) = x^3yz i +xy^3z j + xyz^3 k

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

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

Find velocity and position that has the acceleration a(t)= \langle 3e^t, 18t,2e^{-t} \rangle and specified velocity and position conditions: v(0)=(3,0,-6) \enspace and \enspace r(0)=(6,-1,2)

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 )

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.

Evaluate the integral \int \frac{\log x}{x} \, dx

Let F = (7yz)i + (6xz)j + (6xy)k. Compute the following: A) div F B) curl F C) div curl F (Your answers should be expressions of x, y, and/or z)

Evaluate the Integral \int \tan^2 x \sec^3 x \, dx

Given f'(x)=\frac{\cos(x)}{x} and f(4)=3 , find f(x)

Evaluate the integral \int_1^4 3\sqrt t \ln(t) \, dt

Find an equation of the tangent line to the curve y = x^3-3x+1 at the point (1,-1)

Consider the vector \mathbf F(x,y,z) = (2x+4y)\mathbf i +(4z+4x) \mathbf j + (4y + 2x) \mathbf k . a. Find a function f such that \mathbf F = \nabla f and f(0,0,0) = 0 . b. Suppose C is...

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

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

Evaluate the integral: integral of 2sec^4 x dx.

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

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

Find curl F(x,y,z) , when F(x,y,z) = x^3yz i +xy^3z j + xyz^3 k

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

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

Find velocity and position that has the acceleration a(t)= \langle 3e^t, 18t,2e^{-t} \rangle and specified velocity and position conditions: v(0)=(3,0,-6) \enspace and \enspace r(0)=(6,-1,2)

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 )

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.

Evaluate the integral \int \frac{\log x}{x} \, dx

Let F = (7yz)i + (6xz)j + (6xy)k. Compute the following: A) div F B) curl F C) div curl F (Your answers should be expressions of x, y, and/or z)

Evaluate the Integral \int \tan^2 x \sec^3 x \, dx

Given f'(x)=\frac{\cos(x)}{x} and f(4)=3 , find f(x)

Evaluate the integral \int_1^4 3\sqrt t \ln(t) \, dt

Find an equation of the tangent line to the curve y = x^3-3x+1 at the point (1,-1)

Consider the vector \mathbf F(x,y,z) = (2x+4y)\mathbf i +(4z+4x) \mathbf j + (4y + 2x) \mathbf k . a. Find a function f such that \mathbf F = \nabla f and f(0,0,0) = 0 . b. Suppose C is...

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

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

Evaluate the integral: integral of 2sec^4 x dx.

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

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

Find curl F(x,y,z) , when F(x,y,z) = x^3yz i +xy^3z j + xyz^3 k

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