Suppose a continuous function f is concave up on (- 00,0) and (0, 00). Assume f has a local maximum at x = 0. What, if anything, do you know about f'(0)? Explain with an illustration.

Q: if r = -1 Is f(r) = · continuous at r= - -1? (Show your work using limits.)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Express the limit as a definite integral on the given interval. -дх, [1, 6] (x;)2 + 8 lim n- 00 i =…

A: Given limn→∞∑i=1nx*ix*i2+8Δx and 1,6 We have to express the given limit as a definite integral.…

Q: Every continuous function on a, b\, that has absolute extrema on endpoints, must have one .(a, b)…

A: b. False Consider a continuous function f (x) on [a, b], that has absolute extrema on the endpoints.…

Q: Determine whether the following statement is true or false, and explain why. The absolute maximum of…

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Q: Compute the derivative of f (x) = x3/2 using the limit definition. Hint: Show that

A: we have;  f(x)=x32

Q: Express the limit as a definite integral on the given interval. n eši -Ax 4 + X; lim [0, 2] i = 1

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Q: 1. Show that the function f(x) = 3x + 2 is continuous at (-2, 3). Is it uniformly continuous?

A: As per our guidelines we are mandated to solve only one question at a time please repost the…

Q: Express the limit as a definite integral on the given interval. lim (5(x)3 – 7x]Ax, [2, 6] n- 00 = 1…

A: Consider the given limit and interval. limn→∞ ∑i=1n5xi*3−7xi*Δx and interval=2,6 Now, go through the…

Q: is there any linear independent functions with n – 1th continuous derivative g1, 92, ... , gn(with…

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Q: Find where the function is continuous, but not differentiable..

A: Given,

Q: Express the limit as a definite integral on the given interval. lim [9(x;")³ – 4x;]Ax, [2, 8] i = 1…

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Q: Express the limit as a definite integral on the given interval. n lim -Дх, [1, 8] n→* i = 1 (x;)2 +…

A: Definition of definite integral: ∫abf(x)dx=limn→∞∑i=1nfxi*∆x in the interval [a, b].

Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

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Q: Show that f(x) = is uniformly continuous by definition on the interval (-1,1) . 4 - *

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Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: Express the limit as a definite integral on the given interval. n X;* lim -Ax, [1, 9] (x;*)2 + 8 i =…

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Q: Express the limit as a definite integral on the given interval. lim (2-5(x,)² + 6(x;")³] Ax, [0, 4]…

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Q: Express the limit as a definite integral on the given interval. n lim -Дх, [1, 3] (x*)2 + 8 i = 1 dx

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Q: Show that the function is continuous on  (∞ , -∞).

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Q: Determine if the given (picture attached) is continuous or not at x = 1 and at x = 0.  Identify the…

A: Heavy check the continuity at x = 0 and x = 1 then we identify the discontinuity.

Q: Express the limit as a definite integral on the given interval. -Дх, +7 [1, 6] lim dx J1

A: The following limit is expressed in the definite integral as shown below

Q: Find the derivative of f(x) = 1 at r = 0 using the definition of the derivative as a limit. Va +1 Be…

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Q: Express the limit as a definite integral on the given interval. lim n - 00 -Дх, [1,5] (x*)2 + 6 dx

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Q: Express the limit as a definite integral on the given interval. x; In(1 + x3) Ax, [2, 3] lim 3 dx

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Q: Express the limit as a definite integral on the given interval. lim Ax, [1, 4] (x;)2 + 3 dx Need…

A: Given query is to write the expression as integral.

Q: Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of…

A: suppose that f is continuous function . We have to find the following

Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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Q: Express the limit as a definite integral on the given interval. -Дх, [1,4] (x;)2 + 9 lim i = 1 dx

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Q: Given the piecewise function f(x) = Why is f not differentiable at x = 5? Of is continuous at x = :5…

A: This question is based on continuity of function.

Q: Explain, using limits, why f(x) = - is not continuous at x = 0.

A: To Determine: explain using limits why f(x)=1x  is not continuous at x=0. Given: we have a…

Q: Express the limit as a definite integral on the given interval.

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Q: Let f(x) = 2x³ + 5x, and let a be a number. Compute the appropriate limit to find the instantaneous…

A: Please see the explanation below...

Q: Let ƒ be a function that is continuous on [0, 2] and đifferentiable on (0, 2). Suppose that f (0) <…

A: Yes, we will show that f' necessarily take on both positive and negative values on (0, 2). If the…

Q: Which of the following is always true for integrable functions f and g?

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Q: Express the limit as a definite integral on the given interval. * n Χρισ lim Σ -ΔΧ, [1, 8] 0-00…

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Q: Would it be possible for a function to be continuous on [0,2) but not on [0,2]?

A: Let us consider the function f(x) =(x+4)/(x-2) .

Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, ¤]?

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Q: Express the limit as a definite integral on the given interval. cos X Дх, [Зя, бя] lim 6x X dx 3x

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Q: 8) Assume that 2 + Va if x >1 if x < 1 f(x) = Determine whether or not f is continuous at x = state…

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Q: Express the limit as a definite integral on the given interval. lim 2 x;)?+9 -ах, [1,4] (x;")² + 9'…

A: Use;∫abf(x) dx =limn→∞ ∑n=1n f(xi) ∆x                       over the given interval [a, b].

Q: Does f(x) 1-V1-x² continuous on the interval [-1, 1]?

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Q: express the limit as a definite integralon the given interval

A: Question: Answer:

Q: Express the limit as a definite integral on the given interval. lim (4(x")3 – 3x;]Ax, [2, 6] n- 00 i…

A:

Q: Express the limit as a definite integral on the given interval. lim [9(x,")³ – 4x†]Ax, [2, 6] n- 00…

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Q: Explain the difference between a function f(x) being continuous at the point x=a and the limit…

A: We need to find the difference between function is continuous at x=a and limit exists at x=a

Q: Sketch the graph of a function f that is continuouson [1, 5] and has the given properties. Absolute…

A: Given: The function is continuous on [1,5] The absolute minimum is at 2 The absolute maximum is at 3…

Q: a function is continuous at x = c, then the limit exists as x approaches c. If the domain of a…

A: a. If a function is continuous at x = c, then the limit exists as x approaches c By the definition…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.