21. Determine the following function if continuous at 2x g(x) s6) = ; at x = 3 \x² – 4x + 3 A. discontinuous at x-3 B. discontinuous at x=3 C. continuous at x=3 D. continuous at x=-3

Q: 30. Consider the function defined by 0ifx 1 Sketch this graph and find all points where the graph is…

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Q: - { S 1² – 3 if r -1 2. Determine the constant k such that the function f(r) is continuous at r =…

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Q: ´28 – e14z x 0 Determine whether the function f(x) = 14x – 1

A: Solution: Consider the given function is  f(x) = x8-e14x    x<014x-1       x≥0 To check whether…

Q: 3. If f is continuous and f (x) dx = 8, show that the graph of ƒ intersects the line y = 4 at least…

A: The function f is continuous. The integral function is ∫13fxdx=8.

Q: 7) Calculate the slopes of the following functions at the given points: Ta) f(x) = ln (x²-x + at IL)…

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Q: 8. Suppose the derivative of the function y = f(x) is y' = (x – 1)*(x – 2)(x – 4). At what points,…

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Q: 3 Given the function: f(x) = (1+ x)³/2 . x - 1 Prove that it is increasing on (0, +00) analytically,…

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Q: 1. Given that x +1 2x2-1 g(x) Show that the g(x) function is continuous at a = 4.

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Q: Suppose that the cost of producing x apple is c(x) = 2000 + 100x - 0.1x^2. Find the function f(x)…

A: We will find out the required function.

Q: 19. Determine the following function if continuous at 2 f(x) = (,) ;at x = -1 + 1 A. discontinuous…

A: Explanation of the answer is as follows

Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

A: Consider the given statement "If f is a continuous at x = c, then f has a derivative at x = c".

Q: (x+14 if x S2 5. Let f(x) = x? if x>2 Find the value of k that will make f continuous on (- o, 0).

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Q: 11. Suppose a function is defined so that it has derivatives f'(x)=x²(1–x) and S"(x)=x(2-3x). Over…

A: Given that, the derivatives of a function f is defined asf'x=x21-xf''x=x2-3x We need to find the…

Q: Given the graph of derivative f'(x), find: a) Any interval(s) where f(x) is decreasing b) Any…

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Q: Suppose that the first derivative of f(x) =- is approximated by the following formula 3x+4 -2f(x –…

A: The given problem is to find the actual error of the first derivative of the function using the…

Q: Differentiate the function with respect to the independer X f(x) = +e5x + e 2 e (x) = 0

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Q: 4 Suppose that f(1) = 9, f(4) = -7, f'(1) = 6, f'(4) = -1, and f" is continuous. Find the value of…

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Q: Find a nonzero value for the constant k that makes the function tan(kx) f(x) = 3 3x + 2k2,…

A: Given: f(x)=tan(kx)x,   x&lt;03x+2k2,   x≥0 A function f(x) is continuous at x=a, if limx→a-f(x) =…

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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

A: A function f is said to be continuous at a point x=a if limx→af(x)=f(a).  The left hand derivative…

Q: (3) If the functions f(x) and g(x) are continuous 0sxS1, then f(x)/ g(x) is continuous on the…

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Q: Suppose g: IR - IR is a differentiable function with bounded derivative, Fix e> 0 , and define flx)…

A: to show f is one one we will show that for  x1 not equals to x2 , f(x1) is not f(x2)

Q: Find all values k that make this function continuous at x = 3. 3.x – 9 - if x > 3 x2 3.x f(x) - 3x…

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Q: If we use Simpson's rule for a function f(x) = X +1 with n=4 , then the approximate of S f(x)dx is

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Q: 2, if x 1

A: The given function,  f(x)=1x,if x≤1x2-1,if x&gt;1

Q: In the fucntion:  f(x)= (12-3x)(e^x)  When is the function concave up and concave down in interval…

A: Given,f(x)= (12-3x)(e^x) By definition,

Q: x2-x-1 , if x 1 is 1 if x= 1 continuous at x=1 since the right and the left limits are equal at x =…

A: f(x)=x2-x-1if x&lt;13x3-4if x&gt;11if x=1

Q: 55. Is the function given by S + 4, for x s 3, 2x - 5, for x > 3, F(x) continuous at x = 3? Why or…

A: Function is given by F(x)=13x+4 for x≤32x-5 for x&gt;3 now show that it is continuous at x=3 or not.…

Q: 4ex +x-k if x 0 be continuous everywhere?

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Q: x2 – 1, if x 1 Let f(x) (a) Is y = f(x) continuous at x = 1? (b) Is y = f(x) continuous at x = 2?

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Q: Find the dérivative of the function: f(x)=In(e^x-13x)

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Q: 35. Given that f(z) is a continuous even function, then A 0 D

A: We will use the definition of an even function and properties of definite integrals to find the…

Q: Find the linearizationsof the following functions at x = 0. ln (1 + x)

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Q: 1(a): Find the value of k that makes function continuous at x = 4 4x +8 > 4 4x – k a <4 f(x) =

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Q: if x1 O No, since g(x) is undefined at x=1. O Yes, and g'(1)=3. O Yes, and g'(1)=8. O No, since g(x)…

A: Given

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: Determine if the function is continuous or discontinuous at x = 2. x2 - 1, if x 22 h(x) = 2x-1, if…

A: We have to find

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: 1 Suppose y : [0, x) →R is continuous and order exponential. If L{y} s3/2 %3D and y(0) = 1, express…

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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…

Q: 6. gx) VX- 3 at x = 4 三 7 g(x) at X = 8 三 e1 gCX)= n4ーメ at x =0

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Q: Гa+ 4x ifx 1 Let f(x) (a) The value of a that will make f(x) continuous for all real numbers is a =…

A: Check the differentiability of a function when it is continuous at x= 1 .

Q: 20. Determine the following function if continuous at 2x g(x) = \72 – 4x + 3 . ; at x = -1 A.…

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Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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

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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: .3 Suppose that f is a continuous function and that f(x) dx = 6. Find f(3x)dx.

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