Calculus Answers

Write the following 2-space vectors in Cartesian form:

a . | 𝑢⃗ | = 1 0 , 𝜃 = 6 0 °

b. |𝑣| = 8, 𝜃 = 135°

c. |𝑤⃗ | = 5, 𝜃 = 210°

Find the magnitude and direction of the following

2-space vectors.

a. (−3, 4)

b. (2, 7)

c. (−5, −3)

Differentiate y with respect to X and hence find the gradient of the tangent to the curve

  y=4x² + 3x +2 when x=2

(x^2-3x-4)/(x-4)Factor the numerator of this function. What do you notice about the numerator and denominator of the function, Simplify H(x) and write the new function below as G(x).

 What significant graphical feature is produced when a function like H(x) can be simplified to G(x) ?

 : Graph the function H(x), and clearly state its domain and its range, taking note of the fact that H(x) is not the same as G(x). 

A box with a square base and with height f(x) is to be constructed so that it has a volume of 1000 cubic centimeters. What are the possible dimensions of the box?

Thank you so much!

A leading well panel manufacturer had an year end promotion sale on last December. At the end of the sale they found out that the amount of sales they have done after "x" number of days was; show that the differential equation

Evaluate dy/dx from the equation  when 3xy^2+4x/y-(y-5)/(2x^2-1)=11 when x=1

Integration Procedures (Integration by Parts)

∫ θ cosθ dθ

Integration Procedures (Integration by Parts)

∫csc^(-2)x dx

Integration Procedures (Integration by Parts)

∫ x³dx/cuberoot of (8-x²) from 0 to √7