Find the upper and lower sums for the region bounded by the
graph of the function and the x-axis on the given
interval. Leave your answer in terms of n, the number of
subintervals.
f(x) =
7x2 [0, 3]
Consider the following functions. f(x) = x − 3, g(x) = |x +
3|
Find (f ∘ g)(x).
Find the domain of (f ∘ g)(x). (Enter your answer using interval
notation.)
Find (g ∘ f)(x).
Find the domain of (g ∘ f)(x). (Enter your answer using interval
notation.)
Find (f ∘ f)(x).
Find the domain of (f ∘ f)(x). (Enter your answer using interval
notation.)
Find (g ∘ g)(x).
Find the domain of (g ∘ g)(x). (Enter your answer using...
Find the Taylor series or polynomial generated by the following
functions
a. )f(x) √ x centred at x=4 , of order 3
b.) f(x) cosh x= e^x+e^-x/(2), centred at x=0
c.) f(x) = x tan^-1x^2 , centred at x=0
d.) f(x) = 1/(√1+x^3) , centred at x=0 , of order 4
e.) f(x) = cos(2x+pie/2) centred at x= pie/4
Find the derivatives of each of the following functions:
1. f(x) = (3x^2 + 2x − 7)^5 (2x + 1)^8
2. g(t) = cos(e^2x2+8x−3)
3. h(x) = e^x2/tan(2x−3)
4. Find dy/dx if cos(xy) = x^2y^5
Implement in MATLAB the Newton-Raphson method to find the roots
of the following functions.
(a) f(x) = x 3 + 3x 2 – 5x + 2
(b) f(x) = x2 – exp(0.5x)
Define these functions and their derivatives using the @ symbol.
For example, the function of part (a) should be f=@(x)x^3 + 3*x.^2
- 5*x + 2, and its derivative should be f_prime=@(x)3*x.^2 + 6*x -
5.
For each function, use three initial values for x (choose
between -10...