Question 12) E i) The relationship between E, n, L and g is given by g = Find 2. 4(nL)²" the maximum percentage error in g due to errors of 1% in n and 0.5% in both E and L. ii) Verify that (0, 0) is a critical point for f (x, y) = ka² + y? – 4xy, then determine the values of k when (0,0) is i. a saddle point, and ii. a local minimum point.

Q: 1. Suppose f(-2) = 3, f'(-2) =-4 g(3) = 2, g'(3) = -1 1.1. What is the linear approximation to k(x)…

A: Linear approximation formula is k(x)=k(a)+k'(a)(x-a) Formula of derivative of composition of…

Q: A table of values for an invertible function f, and its derivative f' is given: x f(x) f'(x) | 2 2…

A:

Q: 8. The function f(x)= x³ +bx² +c has a critical point at (-2, 6). Find the constants b and c.

A: We have given function f(x)=x3+bx2+c

Q: The height of a dolphin, h (in metres), with respect to time, t, in seconds is given by the equation…

A:

Q: None

A: SOLUTION.

Q: Question 1 Consider a polynomial y - g(x) with critical points x - a and x - b and g"(x) – 0 = x =…

A:

Q: Problem 4: Perform a first derivative test on the function f(x) = 2x + 6x a) Locate the critical…

A:

Q: Given f'(t) = -0.2t-e-t, compute f(4)-f(1).

A:

Q: 10. Let f(x) = , then f'(x) = -*-4 and f" (x) = (+4)° 2x3-24x %3D x²+4> 10.1. Find the intervals…

A:

Q: 12. Consider the function A(x) = sin(t2) dt. (a) Find A'(x) (b) Find the x-value of the first…

A: Given,

Q: Find a particular solution of the equation y4 -y3 - y" - y' - 2y = 8x^5:

A:

Q: 20 Figure 1: Graph of y = f'(x) for Question 5 The graph of the derivative of a function y = f'(x)…

A:

Q: 5. Consider a metal rod with a temperature distribution (x, t) as a function of distance x along the…

A: Solution:The method of separation of variables is used to solve certain partial differential…

Q: e critical points

A: The given function is f(x,y)=(x2+y2)ex2-y2.

Q: Let h(x) = f(x) + g(x). If f(x) = x³ and g(x) = 4x4, what is h'(1)? Do not include "h'(1) =" in your…

A: Given query is to find the Indicated derivative. h(x)=f(x)+g(x)f(x)=x3g(x)=4x4 The objective is to…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.