Introduction 1. Determine whether the function is even, odd, or neither a. f(x) = 5 – 3x b. f(x) = x - x² – 1 c. f(x) = 2x³ + 3x с.

Q: s] B1(a): Find the value of k that makes function continuous at x = 4 x > 4 6x – k x < 4 3x + 6 f(x)…

A: The given function is fx=3x+6if x&gt;46x-kif x≤4. Assume that the above function is continuous at…

Q: 3x-4 -,x < 1 x+2 4. Given the function f (x) = . Calculate f'(1-) and f'(1+). In?x x+1

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Q: 7. For the function f (x)=(x-2)° +1, a. Sketch the graph of over the interval [0,3].

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Q: Determine the smallest value of the constant a for which the graph of the function f(x) = a^x−x is…

A: Since f(x) should always be greater than x axis ⇒f(x)&gt;0ax-x&gt;0ax&gt;xTake log both…

Q: How can I explain what it means for a function f(x) to be O(1)?

A: The 'f(x) to be O(1)' is to be read as function f(x) is of the order of 1.  Now refer to step two to…

Q: Find the value of k that makes the function continuous. Justify your answer. 2x – 1, x 2

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Q: Suppose ƒ is an even function and Evaluate

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Q: Please I want solution of question 4 with step by step. Many Thanks

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Q: 14). a) Consider the function f(x) = x – 2e-* +1 for x 2 0. i) Show that the function is increasing…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: 1. Consider the function f(x) = -x² + 6x and the point P(2,8) on the graph of f.

A: Given data: The expression for the given function is f(x)= -x2+6x. The given point is A(2,8). (a)…

Q: 2 47) Use the graph of f(x) shown to the right to solve: a) f(x)-0 b) f(x)<0 y-f(x)

A: a) Consider the given function to be y = f(x). Solve the equation f(x) = 0 using the given graph as…

Q: True or False The function f(x) = 2x/(x - 3) has y = 2 as a horizontal asymptote.

A: Given: fx=2xx-3 Concept Used: If degree of denominator is equal to the degree of numerator then…

Q: a. Find the inverse of the function ƒ(x) = mx, where m is a constant di«erent from zero.b. What can…

A: To find :   a) The inverse of the function f(x) = mx, where m is a constant different from…

Q: x² – 4 3. Do you agree with the contention that the functions f(x) = x+ 2 and g(x) =- X- 2 are the…

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Q: 2. The average cost (in dollars) per mile for riding a miles in a cab is c(x)=2.5+2z As x gets…

A: Given that: c(x)=2.5+2xx

Q: 4x+7 18x<2 (ii) If f(x) = , determine whether the function f(x) is continuous 4x-1 2<xs4' throughout…

A: We determine whether the function f(x) is continuous throughout its domain.

Q: What is the change of y with respect to x of the function s(x) = (3x¹ + 9x³)(x² - 6x +9) ? -9x²…

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Q: 3) Let f (x) = e=x² Where is y'> 0? What does this tell you about the original function?

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Q: 1 9. Compare the domains of the two functions g(x) = /r – 2 and h(r) = %3D

A: Question is solved.

Q: 9. Determine the coordinates of a point(s) that do not change between the original and the…

A: Given that: f(x)=-x2+5

Q: 10) What is the domain of the function f(x) = Eo?

A: Domain

Q: B1(a): Find the value of k that makes function continuous at x = 4 3x + 6 x > 4 6x – k x < 4 f(x) =…

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Q: If f(x) is a differentiable function such that f'(-2)=-1 and g(x)=f(3x+1), then what is g'(-1)?

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Q: 5. The coordinates of the hole for the function f (x) x²-4 are: x-2

A: Given function, f(x)=x2-4x-2

Q: a) Let 3x2-1, for x3 f(x)= be a piecewise function. Eevaluate | Fx)dx= b) Let f(x) = 3x-1, for x< 3

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Q: 1. Consider the function f(x) = -x² – 4x – 3 a) Determine f(-4), f(a), and f(a+ h).

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Q: 18. Suppose that a company produces and sells bicycles and that the start-up cost is $3000 and $75…

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Q: 5. Consider the function (x2 + y²)e-¯-. Provide the number of maxima of f(x, y). In case there is no…

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Q: Find the point on the graph of the function that is closest to the given point. f(x) = /x, (3, 0)…

A: Given, y = f(x) = x Let's assume the closest point to (3,0) will be (x, y) then (x,y) = (x, x)…

Q: #2. Determine the equation for piecewise function f(x) given its graph below. -9-8-7-6-5-4-3 f(x) 5…

A: Given data:-

Q: . If x is large, which function grows faster, f1x2  2xorg1x2  x2?

A: To determine for the large values of x, which of the functions f(x)=2x and  g(x)=x2 grows faster.

Q: 3. Armaan claims that the functions f(x) = 32x + 5 and g(x) = 32* + 8 have different instantaneous…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1. Determine if the function is even or odd g(x) = x³ +x, f(t) = 1 + cost

A: Given function are gx=x3+x and ft=1+cost. To determine whether function is even or odd. Solution: A…

Q: 9) Differentiate the following function. Simplify your answer as much as possible. Show all steps y…

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Q: 2 Consider the function f (x) = x + 6x 3 (a) Find the domain of f (x).

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Q: 1 For what value of x does the function g(x) =x³ – 2x² concave downward? %3D

A: Consider the function  gx=13x3−2x2

Q: X+1 5) Is the function given by f(x) x2 - 8x + 15 continuous at x = 3? Why or why not?

A: f(x)=x+1x2-8x+15

Q: 6- For the function y=lnx a- Describe what type of function it is. b- How is the function related to…

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Q: 1 Use the functions given by fx) 1 and g(x) = x' to find (fº g)¯- %3D X - 125

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Q: Find the lineearization L(x) of the function f(x) = x^3/4 at x = 16.

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Q: Q4:- Sketch the following functions showing the detailed steps in different graphs: h) f(x) = |Inx|

A: Sketch the following function showing in the given expression.  f(x) = 1/|lnx|

Q: 3. Do you agree with the contention that the functions f(x) = x+2 and g(x) x-2 are the same in every…

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Q: B1(a): Find the value of k that makes function continuous at x = 4 4x + 6 x > 4 f(x) = 6x – k x < 4…

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Q: 1. Sketch the reciprocal of the function f (x) = x - 6.

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Q: 1. Find when the function is increasing and when it is decreasing. x2 – 9 f(x) = x2 – 16

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Q: 1.) Is f(x)=(2x^3) + (300/x^3) + 4 increasing, decreasing or not changing at x=-2?

A: fx=2x3+300x3+4

Q: 6. What is a point of inflexion ? Does f(x) = x' have a point of inflexion at x = 0?

A: Given that,

Q: 3. Find the value of the constant k that makes the function continuous f(x) = {x² – 6, x + 4k, x 6

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Q: 1. Find the function f given that f'(x) = 2x and f(2) = 5. Is the function ƒ unique? Why?

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Q: does y=e9-x2-2 exist? whaet is the domain and range of the function if exists

A: Given function is  y=e9-x2-2 which is of the form of exponential function and it exist.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.