f(a + h) – (a) 9x2 - 9x + 2, it is easiest to first find both f(a + h) and f(a). We can then To find given f(x) utilize the results to write the desired quotient. We begin by calculating f(a + h). For that, we substitute a + h for x, expand the parentheses, combine like terms, and simplify. f(x) = 9x2 - 9x + 2 (a + h) = 9(a + h)2 – 9(a + h) + 2 9a2 + + 9h2 - 9a - 9h + 2

Q: Sketch the graphs of the functions f and g. f(x) = x +3, g(x) = x² – 9 157 10 -15 -10 5 10 -15 -10 -...

A: Graph of f(x)=x+3 is a straight line which intersect x-axis at (-3,0) and y-axis at (0,3) Graph of g...

Q: Question 10 Find the arc length of the curve y = J8sin()-1 1 dt for -2<x<2. Your answer: o V8 O cos(...

A:

Q: Find the critical points of f(x) = x' – 18x? + 60x and use the Second Derivative Test (if possible) ...

A:

Q: Find dy/dx if y2 = x2 + sin xy

A:

Q: Find the measure​ (in radians) of a central angle of a sector of area 53 square inches in a circle o...

A:  

Q: A function f is said to be invertible with respect to integration over the interval [a, b] if and on...

A:

Q: Explain how to compute the curl of the vector field F = ⟨ƒ, g, h⟩.

A: Here given

Q: Compute the angle between the two planes, defined as the angle 0 (between 0 and n) between their nor...

A:

Q: 2 | (t² + 3) cos(5t)dt 0.

A:

Q: Let g be the function defined by g(x) = -x² + 6x. Find g(a + h), g(-a), g(vā), a + g(a), and . (e)6 ...

A: Since you solved three correctly, so I will show the incorrect ones.  We plug x= sqrt(a) in g(x)  

Q: Solve the problem. 35) Estimate the volume of material in a cylindrical shell with height 28 in., ra...

A: Given data:

Q: 3n Let sn = e 6" be the nth partial sum of an. Select all that apply n = 1 Your answer: Ean= e n = 1

A:

Q: The following is a price demand function for a company that produces and sells themed T-shirts: p(x)...

A:

Q: OA man 6 ft tall walks at a rate of 6 ft/sec away from a lamppost that is 19 ft high. At what rate i...

A:

Q: Including 5% sales tax, an inn charges $252 per night. Find the inn’s nightly cost before the tax is...

A:

Q: g(t) = k/k + t2 where k is a fixed constant. (a) Sketch the graph of g(t) for k = 3. Show all your wo...

A:

Q: Use a linear approximation (or differentials) to estimate the given number. Consider the linear appr...

A:

Q: Six orderings Let D be the solid in the first octant bounded bythe planes y = 0, z = 0, and y = x, a...

A:

Q: Two vectors v and w, each of length 30, lie in the plane x + 2y – 2z = 0. The angle between v and w ...

A:

Q: Vector u has POSITIVE x-component, POSITIVE y-component and ZERO z-component. Vector v has NEGATIVE ...

A:

Q: SOLVE

A:

Q: determine the radius of convergence of the given power series.

A:

Q: Find the point P on the graph of the function yY = /x closest to the point (11, 0) The x coordinate ...

A:

Q: 5

A: We will find the limit of the given sequence as n approaches infinity. 

Q: Fill in each box to make the statement true.(5 + √   )(5 - √    )=22

A: Here given  

Q: Income Tax In a certain country the tax on incomes less than or equal to €20,000 is 10%. For incomes...

A:

Q: Which of the following identities hold? Select all that apply.

A:

Q: Pretend u x v = (0, 3, 2). What is (6u + 3v) × u? A) (0, 18, 12) B) (0,0, 0) C) (0, –9, –6) D) (0, 9...

A: To find the value of the given cross vector.

Q: Maximum Profit A corporation manufactures digital cameras at two locations. The cost of producing x,...

A: Given: Cost of producing x1 units Cost of producing x2 units Profit function is

Q: Find the volume of the solid under the graph of the function f(x, y) = xy + 5 and above the region. ...

A:

Q: Find all the x-values at which the critical points occur of the function f(x) = 5x' – 16x2 + 11x on ...

A:

Q: A box has a square base of side x and height h. (a) Find the dimensions x, h for which the volume is...

A:

Q: lim 4x²+x -27 Find the limmit.

A:

Q: Let  f(x)  =(x- 3)-2. Show that there is no value of  c in (1, 4)such that f(4) - f(1) = f'(c)(4-1)....

A:

Q: A spherical balloon is inflated with gas at a rate of 14 cubic feet per minute. How fast is the radi...

A:

Q: Use partial fractions to find the indefinite integral.

A:

Q: Find the linearization of y : at x = 16. (Use symbolic notation and fractions where needed.)

A:

Q: A new car worth $24,000 is depreciating in value by $3000 per year.a. Write a formula that models th...

A:

Q: 15.5 10.5 • 15.5 Suppose f(x)dx = 3, f(x)dx = 10, f(x)dx = 5. 8, 8. 13 f(x)dx 10.5 (3 f(x) – 10)dx =...

A:

Q: Find all the x-values at which the critical points occur of the function f(x) = 5x³ – 16x2 + 11x on ...

A:

Q: 8.

A:

Q: For each of the given functions y = f (x), a. find the slope of the tangent line to its inverse func...

A:

Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec-1

A: Let, z=(2x+3)/5   We differentiate using the chain rule  

Q: Consider the following simple harmonic motion equation. What is the period of this​ motion?​s(t)=7 c...

A: We compare the given equation with s(t)=a*cos(b(t-c))+d   So, a=7, b= 2 , c=0, d=0   

Q: Find parametric equations for the line through Po = (3, -1, 1) perpendicular to the plane 8x + 5y – ...

A: Consider the point Po and the equation of the given plane. Find the vector Po and the direction vect...

Q: You may recall that the point inside a triangle that lies one-third of the way from each side toward...

A:

Q: x3 The surface area obtained by rotating the curve y = 12 1 +÷, 3<x<5 about the y-axis is

A:

Q: Which of these describes a parametrized line perpendicular to the plane 3x + 2y + z = 15? a) (2+6t,3...

A: The direction ratio of the normal vector to the plane is (3, 2, 1) So the direction ratio of the lin...

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.