Calculus Answers

find fx(0,0) and fx(x,y) where (x,y) not equal to (0,0) for the following function f(x,y) = {xy^3/(x^2 + y^2),(x,y) not equal to (0,0), 0, (x,y)=(0,0)
Is fx continuous at (0,0)?

the function f : x ı→ a + b cos x, is defined for 0 ≤ x ≤ 2π. Given that f(0) = 10 and that f(2π/3) = 1 , find (i) the values of a and b, (ii) the range of f, (iii) the exact value of f(5π/6)

Use the method of Differentiation from the first principle to prove that the
the derivative of the square root of x is given below
d/dx x^1/2=1/2x^1/2

Let f (x) = sin(ax + b) and let g (x) = cos(ax + b) where a and b are constants. Gues a formular for f*(x) and g"(x) for general n (positive integer )

Silver ore was found in a region. Then, as a result of the investigations, silver reserves in the region were estimated to be 50000 tons. Later, a mine was established in the region and silver reserves in the region began to be mined. According to the amount of silver extracted from the mine, e (-t / 40000), the rate of change depending on time t time. Under the assumption that the technology will not change, find the number of tons of silver that cannot be removed from this mine.

The logistic growth model formula is given by
〖ye〗^kt+Ay=〖Le〗^kt
Where y I the population at time t(t≥0) and A,K and L are positive constants.
Use implicit differentiations to verify that
dy/dx=k/L y(L-y)

(d^2 y)/〖dt〗^2 =k^2/L^2 y(L-y)(L-2y)

Evaluate the integral
Intergral xsquared +1over square root of xcubed +3x whole thing to dx
using appropriate substitution.

Use logarithmic differentiation to solve dy over dy, if y = xsquared square root 7x-14 over (1+x) to the power 4

Find the volume of the solid that results when the region enclosed by

Even if both the partial derivatives of R → R
2
f : exist at a point )b,a( , the
function f may still not be continuous at )b,a( .