Calculus Answers

lim x ➡0 (lim y ➡0 for ysinx/|x|) does not exist. Say true or false

The range of the function f(x, y) =√81-9x²-9y² is [0, 8] . Say true or false.

The function f(x, y) ={x²y/x⁴ +y² , (x, y) ≠0 and 0 , (x, y) =0 }is not continuous at (0,0).

Say true or false.

If f(x, y) ={ 1 if x=0 or y=0 and 0 otherwise } then lim f(x, y) does not exist for limit (x, y) approaches to (0, 0).

can the product rule be used to verify the chain rule? support your answer with example.

The function f defined by f(x) = tan(2x) is a periodic function with period π. ii) The function 𝑓:𝑹 → 𝑹, defined by 𝑓(𝑥) = 1 − |𝑥| is differentiable at x=1. iii) The function 𝑓: [3,4] → 𝑹 defined by 𝑓(𝑥) = 𝑥 ଶ − 𝑥 is monotonic in its domain. iv) Every continuous function is differentiable. v) Every curve over R has a point of inflection. 

Faced with two distinct demand functions:

Q1=24-0.2P1

Q2=10-0.05P2

Reduce the quadratic form X2+3Y2+3Z2-2yz to the canonical form through orthogonal transformation

Determine the value of a and b so that lim(x→0) (asin2x-bsinx/x³)=1