Let h(x) be a differentiable function on R. Use MVT to find an upper bound for h(1998) if h(-2) = 2 and h'(x) is at most 1 for all x in R.

Q: Is f(x)= Vx + 1 continuous at x == -1

A: Draw the graph and check continuty with help of limit of function.

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

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Q: Express the limit as a definite integral on the given interval. lim > x; In(2 + x;2) Ax, [2, 5] n-…

A: The solution is given below

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A: Given problem:- Is the function ex/cosx continuous on the interval [0, π] ?

Q: Express the limit as a definite integral on the given interval. n lim x, In(2 + x;²) Ax, [0, 3] j=1…

A: Given: The limit limn→∞ ∑i=1nxiln2+xi2∆x on interval 0,3 To determine: The interval notation of…

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

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Q: Express the limit as a definite integral. n 7 lim 2 3x Ax: [2,7] Ax,0 k= 1 O A. 3x' dx 2 о в. 3x'd…

A: We have to express the given series as a definite integral.

Q: Express the limit as a definite integral on the given interval. n lim x, In(2 + x,-) Ax, [0, 4] i =…

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Q: Express the limit as a definite integral on the given interval. [4(x;")3 – 4x;1Ax, [2, 7] lim i = 1…

A: Solve the following

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: If f(x) is continuous at x=a , then f(x) is also differentiable at x=a.

A: " If F(x) is continuous at x=a then f(x) is differentiable at x=a." The condition for the function…

Q: Express the limit as a definite integral on the given interva lim [2(xf)³ – 5x¡]Ax, [2, 5] n- 00 i =…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In (In 5x) O A. 1 5x ОВ. 1 x…

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Q: Express the limit as a definite integral on the given interval. lim x, In(2 + x,') Ax, [0, 3] n- 00…

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Q: Let g (x) = f' (x) be a continuous function. If the derivative of the continuous function g (x)…

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Q: Express the limit as a definite integral on the given interval. lim X; V 4 + x3 Ax i = 1 [2, 3] n-…

A: Given the limit limn→∞∑i=1nxi4+xi3∆x in the interval [2,3]

Q: Express the limit as a definite integral on the given interval. cos(x) lim Дх, [Зл, 4л] X; i = 1 dx

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Q: Let f and g be continuous on the closed interval L0,5]. suppose that J s(x)dx=A, / f(x) dr=B, The…

A: Here, to evaluate: ∫35(f(x)-g(x)) dx

Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: Evaluate f x2 dx using the limit defintion of the definite integral.

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Q: Find the derivative of f(x) at r = 0 using the definition of the derivative as a limit. %3D Va +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: define the function at 5 so that it becomes continuous at 5.

A: First, we rationalize the function, so that it becomes continuous at 5 which is shown on the board

Q: Let h(x) = f(g(x)), where f and g are differentiable on theirdomains. If g(1) = 3 and g′(1) = 5,…

A: Given: Let h(x) = f(g(x)), where f and g are differentiable on theirdomains. If g(1) = 3 and g′(1) =…

Q: Express the limit as a definite integral on the given interval. [2 - 5(x,")2 + 6(x,)³] Ax, [4, 8] n-…

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Q: Suppose that fx) is continuous on [0, 9] and F(x) is an anti-derivative of f. If F(0)=9 and F(9)=7,…

A: Given that:                           f(x) is continuous in [0, 9].…

Q: Use the prové thát 1 x| < ]x| fór áll * # 0. onclü X| S x| för åll x € R. Hint. Apply MVT to f(x) =…

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Q: Use limits to determine if f(x) = 1 is continuous at x = 0. (z+2)?

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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: Determine the largest interval over which the fu Vx+2 is continuous.

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Q: Express the limit as a definite integral on the given interval. cos(x) Дх, [2л, Зл] X; lim Зл dx 27

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Q: Express the limit as a definite integral on the given interval. lim Ax [О, 6] 9 + X; i = 1 dx

A: The answer is found in step-2

Q: that makes y continuous but not differentiable by writing the required procedures to that If: X≥0…

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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: Show that the function below is continuous at x 0 (cos x-1 f(x) D if x<0 5x, if x20

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Q: The improper integral f(x)dx can be written as lim f(x)dx + lim_ f" f(x)dx . w--00 w+00 If f(x) =…

A: use the above definition of improper integral

Q: Express the limit as a definite integral on the given interval. cos(x;) Дх, [Зл, 4л] Xi lim i = 1 4л…

A: By definition of definite integral as limit of sums is

Q: Express the limit as a definite integral on the given interval. x, In(2 + x) Ax, [0, 2] lim dx

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Show that the function f(x) = csc(x) is not uniformly continuous on (0, pi/2]

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Q: Express the limit as a definite integral on the given interval. lim Σ Σ x;* -ΔΧ, [1,4] 0-700 (x;*)2…

A: To express the given limit as a definite integral.

Q: Suppose that f(x) is continuous on [0, 9] and Fx) is an anti-derivative of f. If (0)=9 and F(9)=3,…

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Q: Express the limit as a definite integral on the given interval. exi Ax 3 + x; lim [0, 4] dx

A: We need convert summation in to integral

Q: Express the limit as a definite integral on the given interval. n -Ax, (x;")2 + 6 [1, 5] lim i = 1 5…

A: Given query is to express the limit as definiye integral.

Q: Express the limit as a definite integral on the given interval. cos(x;) lim n-0 i = 1 Дх, [2л, 5л]…

A: Given limn→∞∑i=1ncos(xi)xi∆xi in the interval [2π,5π]We need to express the limit as a  definite…

Q: Express the limit as a definite integral on the given interval. lim x; In(2 + x²') Ax, [0, 2] i = 1…

A: Given, limn→∞∑i=1nxi ln2+xi2∆x And interval 0, 2

Q: If f is integrable on [a,b], show by example that F (t) = | f (x) dx is continuous but need not to…

A: We need to show by an example that if f is integrable on [a, b], then F(t) (as defined in the…

Q: Express the limit as a definite integral on the given interval. x;* -Ax, (x;')² + 2 lim n- co [1, 6]…

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Q: d. Use the limit definition of the derivative, f (x) = lim f (x+h)-f(x) 1 +h)=j, to prove that VT =…

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