Consider the following functions. f(x) = x3 and g(x) = - 4x Step 1 of 2: Find the formula for (x) and simplify your answer. Answer Keybo

Q: What value should be assigned to a to make the function S(x) = (x²-1, x<3 (2ax, x 23 Continues at…

A:

Q: Given the function h (x) = -v2 – x, what is h (x)?

A:

Q: Which of the following functions grow faster than x2 as x→∞?Which grow at the same rate as x2? Which…

A: We will find the limit  x→∞ of the ratio of the two functions.

Q: Write a derivative formula for the function. f(x) = 8x√(7x+2) +91

A: Given,

Q: Consider the following function: -4x – 7 f(x) : x +5 Step 1 of 2: At what x-value is the function…

A: The given function is fx=-4x-7x+5. Rational functions are continuous everywhere except when the…

Q: How are the functions f and g given by f (x) = (1.05)ª and g (x) = eº.05z similar? How are they…

A:

Q: Given the function, find the derivative f (x) = -()" 3z 4 3z- 3 12() 3z-4 O None of the Above

A:

Q: Write the formula for the derivative of the function. f(x) 12x4 19x3 4 f'(x)

A: The function is given by,

Q: Differentiate the following function. f(x) = x° e 9x f'(x) =D

A:

Q: Differentiate the following function. 6 f(x) = 12 e

A: Our Aim is to differentiate the function given below:f(x)=12ex6 -(i)

Q: Which of the following functions grow faster than x2 as x→∞?Which grow at the same rate as x2? Which…

A: fx=x2  &amp;  gx=2x Concept used: Let fx &amp; gx be positive for x sufficiently large. fx grows…

Q: Given the one-to-one function defined by f(x) = Vx – 4 + 1- write an equation for f -1(x).

A: The given one-to-one function is To find the inverse of f(x), replace f(x) by y. Now interchange…

Q: Using the definition of the derivative, find f'(x) for the following function. 4. f(x) = - x² + 8x -…

A: Given: f(x)=-x2+8x-15

Q: Express the following functions in terms of function f where y=f(x). The values of function g are…

A:

Q: Find ƒ‴ (x) , the third derivative of ƒ, and ƒ (4) (x) , the fourth derivative of f, for function.

A: To Determine: The third and fourth derivative of fx=x2x+1

Q: xg x9-₂x = 1 4

A:

Q: Which of the following functions grow faster than x2 as x→ ∞?Which grow at the same rate as x2?…

A: Let, fx=x2gx=1.1x Now, If limx→∞f(x)g(x)=1     →both function are growing with the same…

Q: Find the third derivative of the function f(x)=8x^7/2. Simplify so there are no negative or…

A: Given query is to find the derivative if the expression.

Q: Find f(3) for the given function. f(x) 3D (x- 2)(x- 4)(x+5) Type your numeric answer and submit

A: f(x)=(x-2)(x-4)(x+5)Substitute x=3 in f(x)

Q: а. у%3 (2х* — 7).(3x? + 4)* -

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Express the function h(x)=1x−9h in the form f∘g. If g(x)=(x−9), find the function f(x).

A: Topic = Functions

Q: Find the value of k, if the constant k that makes the function continuous:

A: Given,          f(x)=x2+k2if x≤4kx+12if x&gt;4

Q: Write a derivative formula for the function. f(x) = (5x + 29)5(15x + 2)

A:

Q: Find the second derivative of the function. f(x) = 9(5-2x)4 f"(x) = Submit Answer

A:

Q: Write the formula for the derivative of the function -4 g(x) x2 = g '(x)

A: Formula:

Q: Calculate the output for the function with he given input. If there is no possible output for the…

A: The given function isfx=xx-1. Here function fx is not defined if x-1=0. x-1=0x=1 So, the function is…

Q: Write a derivative formula for the function. f(x) = 2xV9x + 6 + 95 %3! f'(x) =

A:

Q: Express the function h(x)=1/x+7h in the form f∘g. If g(x)=(x+7), find the function f(x).

A:

Q: Find the derivative of the function. Simplify and express the answer using positive exponents only.…

A: Given function is Differentiating with respect to x using product rule of differentiation

Q: Find a formula for a function that f(x) =

A:

Q: Differentiate the following function.   y = xex2

A:

Q: Find the derivative of the function. 36 9 h(x) = 27x² 9 X

A:

Q: Differentiate the following function. f(x) =x° e 10x f'(x) =O

A: Topic :- Differentiation

Q: h(x) = In (a- 7) (r +3)

A:

Q: Find a formula for the derivative of the function 2x2 – 3

A:

Q: Use the appropriate Derivative Formula for the algebraic function below. x2+1 2. y = x2-1

A: y=x2+1x2-1In this we use quotient rule QUOTIENT RULEy=uvdydx=v.dudx-udvdxv2apply this rule in given…

Q: Use an applicable rule to find each derivative. 1. f(x)=x²-2x' +7x-12 2. g(x) = 3x +2x+1 3. s(1)…

A:

Q: If h(x) 6.x + 1, find h(). Is h a one-to-one function?

A: If h(x) = 6x +1. To find h(1/2). Also, to check whether h is a one-to-one function.

Q: Find the first and second derivatives of the following functions and use them to sketch a graph. f…

A: Please refer to the image below

Q: g(x) = = 2x – 4x2 + 13

A:

Q: Express the function h(x)=1x+7 in the form f∘g. If g(x)=(x+7), find the function f(x)

A: Given,

Q: Write the formula for the derivative of the function 7x215x +9 k(x) (Hint: Rewrite as three separate…

A: Given function is

Q: Find the indicated derivative for the function. -5 -6 h'(x) for h(x) = 6x 4x h''(x) =

A: Given: hx=6x-5-4x-6We need to findh''x=?

Q: Write the formula for the derivative of the function. f(x) 7x-0.7 f'(x) =

A: To comute the derivative of the given function y=f(x)

Q: Determine h(x - 1) for the following function. - 2x h(x) %D x2 - 8x + 15

A: The function is an expression, which gives output values (function values) for each inputs which are…

Q: consider the following function  f(x)=x4+4x3+11 a) make a sign diagram for the first derivative.…

A:

Q: Consider the following functions. f(x) = x and g(x) = x2 – 10 Step 4 of 4; Find -(-2).

A:

Q: find the derivative h(x) = 2 x2 − 8 x8 + 6 x

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.