3. It is a fact that if you take a tube and fill it with liquid, the liquid will rise and fall based on the temperature. Assume that we have a tube of liquid, and we have a function h(T), where h is the height of the liquid in cm at temperature T in °F. I. It is true that h(32)=1. What does that mean in physical terms (interpret the units)? Describe the inverse function h'. What are its inputs? What are its outputs? What would the function notation look like (don't use h' because that would be confusing)? What does it measure? II. There is a devise, currently available at your local drug store, that measures the function h'. What is the name of this devise? III.

Q: After a recent flood the water level of a river is 43 feet, measurements show that it is receding at…

A: Given, W = fd = -3d +43  We have to find the formula for inverse function

Q: If F is a derivative function, obtain the derivative of the function u(x) = (F(x))² in terms of F…

A: given u(x)=4x2-12u(x)=F(x)2to find derivative of u(x)

Q: Differentiate the following functions: 6. y = csc-(2sinx)

A:

Q: 0.0 2 -0.5 -2 -1.0 2 I II III 2. 2.

A: In I: the function is less than 0 for some and later greater than 0. The function is increasing…

Q: 2. In a study on the speed of muscle contractions in frogs under various loads it has been found…

A:

Q: .x = t² – 2t – 11 and y = t(t – 4)³ – 3t²(t – 4)² + 7

A: Given:- x = t² - 2t - 11 and y=t(t-4)³ - 3t²(t-4)² +7 To find:- y'

Q: Differentiate the function g(x) = 6x² + 11tanx.

A: The function is given by gx = 6x2+11tanx To evaluate: The expression of g'x

Q: a.) A sphere shaped balloon is being inflated with a rate of 800 cm³ per minute. When the radius of…

A:

Q: Given that h"(w) = -34. State the function that best describes h'(w). O a. h'(w) = -34w O b. h'(x) =…

A: Use the concept of power rule of derivative and select the option form given.

Q: Differentiate the function g(x) = 2x² + 5tanx. Answer g'(x) =

A: Given : the differenctiate Equation : g(x)=2x2+5tan(x)

Q: II. Find the first, second and third derivative of the function s = 3(8t" – 7)"

A: s = 3(8t4-7)4

Q: 8. Find the second derivative of the function: y= (X+1)-x+Y+2 sin ²x

A: The given function is  y=X+1·x+Y+2sin2x

Q: 1. x = 4t3 – t2 +7t and y = t – 6

A:

Q: g(b)= g'(b)= Calculate g(b) and g'(b) where g(x) is the inverse of f(x) - 18, where b 248

A:

Q: What happens to the function f (x) = x² when it becomes f'(x) = x² – 3? It moves 3 units to the…

A:

Q: Differentiate the function L(x) = -6e"(cscx + 7cotx). Answer L'(x) =

A: Given Equation : L(x)=−6ex(csc(x)+7cot(x))   L'(x)= derivative of L(x)

Q: Simplify the function, then find the derivative. f(x) = ln (x√x² - 1)

A: Given:We are required to find:

Q: Estimate the slope of the tangent line of the function y(x) = 24 at x = 1. 2+x (Use decimal…

A:

Q: Calculate the derivative. g" (0), g(s) = es S+7 (Give an exact answer. Use symbolic notation and…

A:

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.