Calculus Answers

Find the 4th left, right, and midpoint Riemann sums of the following functions with respect to particular partitioning of the given intervals. (a.) 𝑓(𝑥) = 𝑥 3 𝑜𝑛 [0,1] (b.) 𝑓(𝑥) =𝑠𝑖𝑛 𝑠𝑖𝑛 𝑥 𝑜𝑛 [0, −1]

Let f(x, y,z) = e √ z−x 2−y 2 . (a) Evaluate f(2,−1,6) (b) Find the domain of f (c) Find the range of f

Your task is to discuss the concept of supremum and infimum for real numbers. Here are some hints on what your presentation can cover.

1. Give the definition of supremum and infimum for a nonempty subset of R.

2. Provide some examples to illustrate the concepts of supremum and infimum.

3. Discuss the Completeness Axiom.

4. Find some standard exercises pertaining to supremum and infimum and discuss its solution. 5. State and prove the Archimedean Property using the Completeness Axiom.

use Lagrange’s Multiplier method to find the maximum and minimum of f(x,y)= y^2 - x^2 subjected to the constraint of 1/4 x^2 + y^2 = 1

The derivative of y = ln 3x 4

Evaluate"\\intop\\intop" x²+y² +2

Where Ris bounded by x²+ y² =1

Discuss the applicability of Calculus in Engineering.

lim ( tan x) = ∞

x→π/2

True or false with full explanation

The function fog exists for the functions f and g , defined by

f(x)= sin t, t∈ R

g(x,y)= x^2+ 5xy + y^2, (x,y)∈ R^2

True or false with full explanation

Find the derivative of y = ln 3x 5