Determine if the following function is continuous at the indicated number. 3. g(x) = { ( 3 – x, x <1 %3D x² + 1, x >1 a = 1

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A: Since, you have posted multiple questions, but according to guidelines we will solve first question…

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A: Let the function f(x) = | 9x | Consider the definition of the derivative, limh→0f(x+h)-f(x)h Here,…

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Q: 1) Draw a rough sketch of a continuous function, ƒ(x), with all the following properties: A) ƒ(0) =…

A: A) f(0)=4 , f(5)=-1, means that points (0, 4) and (5,-1) lie on the function B) f'(0) =0, f'(5)=0…

Q: Q1. (a) Show that the following function is continuous at x = 1 for all values of p. Spx + 1, if x…

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Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A:

Q: For what values of a is the following function continuous for all x? Show the work. a²x +4a if x >…

A: See the attachment.

Q: Q1. (a) Show that the following function is continuous at x = 1 for all values of p. spx + 1, if x >…

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Q: 8. Order the following functions from slowest growing to fastest growing as x→∞. a. 2* c. (In2)* b.…

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Q: Consider the following function. F{x) = x3/2 Find its average rate of change over the interval [4,…

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Q: Q1. (a) Show that the following function is continuous at x = 1 for all values of p. spx + 1, if x >…

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A: Given       y = ln(x + 7)

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A: Concept: L'Hospital rule:Let f and  g be functions that are differentiable on an open interval (a,b)…

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A: K=3 makes f(x) continuous.

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A: given,         limx→∞x3e2x

Q: 1) Find the value of Z that make the function continuous at x=4? V-2 x + 4 X-4 f(x) = {z3 x = 4

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Q: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

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Q: h) f(x) = ln (xe³z)

A: We will use the chain rule of differentiation and the product rule of differentiation to…

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Q: 1. Where are the following functions continuous? x F(x) = ex + 4-x3 G(x) = 3x5 - 4x? H(x) = x-5x3…

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Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A: limx→∞lnx3x=limx→∞3lnx2·1x1    By using L'Hospital's rule=limx→∞3lnx2x=limx→∞3·2lnx·1x1    By using…

Q: S x2 – 3 |kV5+x _if x > –1 if x < -1 - 2. Determine the constant k such that the function f(x) : is…

A: As per our guidelines, I can answer one question and maximum three subparts of a question. Since you…

Q: Given the graph of the f(x) shown below, which one of the following statements regarding the…

A: When we take the absolute function f(x), there will be no part below x -axis, so

Q: (a) At 12 noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/ hour and ship B is…

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Q: Consider the following function. f(x) = x3/2 Find its average rate of change over the interval [1,…

A: The objective is to find average rate of change over the interval [1, 16].

Q: 3. Use the given graphs of the first and second derivative of a continuous function to answer the…

A: To find:- From given graph A. Set up a number line to represent where f'(x) is positive, zero, and…

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Q: Given the function f(x) = x2/3, which of the following is a valid formula for the instantaneous rate…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 9. If f(5) = 13, f' is continuous, and f'(x) dx = 16, what is the value of f(6)?

A: Use property of definite integration

Q: 1. Find the absolute extrema for the following function over the given interval: f(#) = * - + 2 +2…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 8. For what value of the constants A and B is the function f continuous on (-∞, ∞)? Ar + B for x 2…

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Q: 1. Use the following formula (1) to evaluate derivative for each of the functions below: f(x+ h) -…

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Q: Consider the following table of values for the function f (x) = Vx - 2. %3D Point f(x) A -2 -3.26 -1…

A: The table of the values for the function fx=x3-2 is To evaluate: The average rate of change over…

Q: 9) Given the function f(x)=-3x+2 , find the net signed x-axis over the interval [-5,3]. area between…

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Q: Find the linearizationsof the following functions at x = 0. tan x

A: Linearization is tangent line at a point x=atangent equationy-y0=mx-x0m=f'a

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.