Question 3 Find two functions f(x) and g(x) so that h(x) = (fog)(x) a) h(x) = (2x +3)². %3D

Q: Question 4 The relative rate of change of a function f is given by the ratio The relative rate of…

A: relative rate of change of function f is given by f'f

Q: Solve the problem. 5) The function given by y = f(x) shows the value of $6,000 invested at 5%…

A:

Q: QUESTION 4 The derivative of the function f(x) = a' +5 a2 +4 - 4 at a = 0 is 36 -3 O 4 O 129 O 17 61…

A:

Q: f(x) =

A: Given: We have graph of the function. to find:  The function of the graph.

Q: QUESTION 20 Find the critical values of the function below. 9. f(x) =

A:

Q: Question 8: Consider/f = f(p(t)); ƒ is nonlinear function of p(t); derive nonlinear population…

A: The differential equation for non linear population growth model is defined as, 1pdpdt=a-bp where,…

Q: Question 3 .2 If dx F(x)=f(x) and F(– 1) = F(2)= –5, then f(x)dx%3D

A: To solve the following problem using fundamental theorem of Calculus

Q: Question 17. Use logarithmic differentiation to find for the implicit function dx (1+x)5 (1– y)**…

A: We use implicit differentiation and properties of logarithmic function to answer the given question.

Q: c) y = (x-2) 3 x² (x-1)(x+5)4 [Hint: use logarithmic differentiation]

A:

Q: Alog f(x) = log[1+ Af(x), f(x)

A: We have to solve given problem:

Q: Question 5 Assume that dx = 3, f(x) dx = e, g(x) dx = -3, g(x) dx = , and f is an odd function and g…

A:

Q: Question 2: The definition of the exponential function involving the limit of h going to zero…

A: The function is fx=ex. Differentiate it: f'x=ex Then at c = 0.01, f'0.01=e0.01≈1.01 Perform…

Q: THEOREM 3.7 Derivative of the Natural Exponential Function \frac{d}{d x}\left[e^{x}\right]=e^{x}

A: To Show: ddxex=ex Concept: i. ddxfx=limh→0fx+h-fxhii. L-Hopital's Rule:if limx→cfxgx=00, ±∞±∞,…

Q: Question 7 Integrate the function. x + 6 dx *+3Xx +5) (A (x+3)3 X +5 +C x+5 X+3 (x+3 X+5 x+ 3)3 In X…

A:

Q: QUESTION 2 Find the range of the function f(x) = x² + 12. %3D ys 12 Oy2 12 X 20 y 0

A:

Q: QUESTION 3 Provide the slope of the line tangent to f-(x) at the point (-2,1) where f(x)= x5 +2x³ -…

A: slope of tangent line on  f-1 (x) is the derivative of f-1 (x) at the given point .

Q: The graph shown below is f(x) = 3x - 2. X If g(x) = f(t) dt, what is g'(-1)? f*

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: f(x + h) – f(x) h\1/h log 1 + If f(x) log, x, show that = h + 0. h

A: fx=logax

Q: QUESTION 4 · Which of the following is a valid formula for the instantaneous rate of change of the…

A: The instantaneous rate of change of function f(x) is given by f'(x)=limh→0f(x+h)-f(x)h

Q: ns Question 1 alendar eet lim 3x x+5' Evaluate ve O 3 O 00 O 1 Question 2 Differentiate the function…

A: topic - limits and derivatives 1.) 3 2.) 18x2 -9 3.) -h-3

Q: Question 8 Graph the function f(x) = u₂(x) ln x + u5(x) (ln(10 − x) – ln x) -

A:

Q: QUESTION 9 The function f(x)-x2-1, ,is increas OA (-0,-2)U (0

A: We have to  choose the correct answer

Q: Question 5 Describe the long run behavior of f(x) - 5(3) – 4 %3D As - O0, f(x) → |? v As a 00, f0 >…

A: See the attachment

Q: A person’s life expectancy can be modeled by the function g(x) = 10.761 ln(x + 1) + 27.98, where…

A:

Q: Question 425 2 dt, what is F' (x)? (Do not include "F' (x) =" in your answer.) In (t) If F(x)…

A:

Q: QUESTION 8 If (fog)(x) = 6x + 3 and f(x) = 2x - 1 then g(x) = ? O 3x + 2 O 2x + 3 O 3x - 2 O 2x - 3

A:

Q: Question 3 Given f (x) = 2x and g (x) = 4x + 3. Evaluate g (f (-)). (E)

A:

Q: Question 6 The following function is homogenous of degree what? Vx++x²+y? x+y other/not possible 2 4…

A: For the detailed solution of the problem follow the next step.

Q: Question 4 The relative rate of change of a function f is given by the ratio The relative rate of…

A: Given : The relative rate of change is given by the ratio f'/f

Q: Question 3 Suppose that f satisfies | f(x) dx = 6 and 1| f(x)dx= –4. Calculate -5 (2.x + 10 – f(x))…

A: Given that: ∫-53f(x)dx=6 and ∫35f(x)dx=-4

Q: Question 11 > A 25-year-old woman burns 400 – 70t cal/hr while walking on her treadmill. Her caloric…

A: We will integrate the given function

Q: QUESTION 3 Find all positive numbers b such that the average value of the function g(x) = 80 + 5 x -…

A:

Q: Question 10 of 11 A car travels along the highway to Yuma at a steady speed. When it begins, it is…

A: When x= 0 , y= 400  When x= 7 , y= 50

Q: Below are data on the population of a species of moths that inhabit an island and breed annually…

A: The probability is the equal chance of occurrence of observation can involve in the sample or event…

Q: QUESTION 17 The derivative of f(x)=2x2 +3 if a=0 O AX 2h O an 4h O O

A:

Q: 66) y = f(x)= 1-x

A: f(x)=x21-x x-1=0 x=1 vertical asymptote at x=1 Now make a table for graphing x…

Q: Question 7 Differentiate the function. x2 - 4x f(x) : x + 2 -x2 – 4x – 8 A f'(x) (x + 2)2 х? + 4x —…

A:

Q: In Example 6 in this section, we were given f(x) = 3x2 + 2x + 11 and found f'(x) = 6x + 2. (a) Find…

A: Differentiating with respect to x, we get

Q: Question 2 Find the second derivative of the function f(x) = x² - 3x and choose the correct answer.…

A: To find the second derivative of the given function.

Q: Question.1: Let X have a logistic distribution with pdf e f(x) (1+e~")² Let Y e be a transformation…

A: Given :  X have a logistic distribution with pdf,  f(x) =e-x(1+e-x)2 ; -∞ < x < ∞ let Y = ex…

Q: Question 9- Determine the value of the constant k that makes the function in the following…

A:

Q: Question 1 of 14 View Policies Current Attempt in Progress 15 Use the figure below to estimate…

A:

Q: Chapter 4, Section 4.1, Question 036 The figure below is graph of a derivative f'. Select all of the…

A: Observe where f'' is zero

Q: Question 8  what does f(x) = ___

A: Explanation: Given graph looks like an exponential function it is going negative infinite when x…

Q: 4. [3 f(x) – g(x)] dx a

A:

Q: 4. Use logarithmic differentiation to find a formula for f'(x): (x+ 1)3/2(x – 4)5/2 (5x + 3)2/3 |…

A:

Q: Question 2.If y is a function of x, then d(y³) dx is equal to: (A) 3y? (B) За? (C) 3y?y (D) None of…

A:

Q: Question 1: Differentiate the functions. a) f(x) = 2 – 5cosx +x4 + 3* b) f(«) = +

A: I am attaching image so that you understand each and every step.

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.