Calculus Answers

Given: x = e^2t - 1 and y = e^2t + 1. Find y’.

Given: x = 2t + 1 and y = 4t - 1. Find y’.

Given: x = cost and y = tsint + cost. Find y’.

Given: x = csct and y = cott. Find y’.

Given: x = 1 - cost and y = 1 - sint. Find y’.

discuss the continuity of function f(={sin x/x and 1 at x=0

let x1=1 and Xn+1=squrrt(3xn)for all n€N show that (xn) is bounded ,monotone and converges to 3

Write an example of a function whose derivative can be found by using the following rules:

a) Product rule and special function differentiation rules

b) Power rule, quotient rule, and chain rule

c) Chain rule twice

d) Implicit differentiation and special function differentiation rule

1.if f(x)=x^2-1/1+x^2,find f(-1),f(2),f(1/2),f(tan x).

2.graph the surface area of a cube as a function of the volume of a cube.

The equation for a distance, s(m), travelled in time t(s) by an object starting with an initial velocity u(ms-1) and uniform acceleration a(ms-2) is: 𝑠=𝑢𝑡+12𝑎𝑡2 The tasks are to: a) Plot a graph of distance (s) vs time (t) for the first 10s of motion if 𝑢=10𝑚𝑠−1 and 𝑎=4𝑚𝑠−2. b) Determine the gradient of the graph at 𝑡=2𝑠 and 𝑡=6𝑠. c) Differentiate the equation to find the functions for i) Velocity (𝑣=𝑑𝑠𝑑𝑡) ii) Acceleration (𝑎=𝑑𝑣𝑑𝑡=𝑑2𝑠𝑑𝑡2) d) Use your result from part c to calculate the velocity at 𝑡=2𝑠 and 𝑡=6𝑠. e) Compare your results for part b and part d.