For every continuous f:[0,+0) →R _function , if a>0 2fx'f(x*)dx =[ xf(x)dx Demonstrate that this equaiton is correct.

Q: Express the limit as a definite integral on the given interval. cos(x¡) Дх, [Зл, бл] Xi lim бл dx…

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Q: 2 dx 2-x

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Q: what is sin(3t)dt with upper limit of pie/3 and lower limit of 0?

A: Integration of sinat is -cosat/a

Q: Verify that L'Hopital's Rule applies and evaluate the limit.

A: On directly substituting the limit, the indeterminate form 00 is obtained, so we need to apply the…

Q: 5 Find a limit equal to In(2x – 1) dx.

A: We know that, ∫lnxdx=xlnx-x+C…

Q: Use L' Hopital's Rule to find the limit as x approaches positive Inifinity of:  ln(x)-ln(1+x) Hint…

A: Given ln(x)-ln(1+x)

Q: In 0 lim 0 → n sin O cos 0 — In n

A: This question is taken from the Limits in which we have to find the limits of the given question by…

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: Limit as x approaches 0 1-cos(x)/sin(x)

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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: What is the limit as x approaches 0 of 2x/sin(2x)? Do so without using L'Hopital's Rule.

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Q: The midpoint rule cannot be used when the upper limit of the integral results in a singularity of…

A: QUESTION IS BASED ON INTEGRAL CALCULUS

Q: Evaluate the limit using the L'Hopital's Rule. 1 - cosh x lim x→0+ ln(x² + 1)

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Q: Q3: (a) Find the following limits if exist (without using L'Hopital's rule):- 9-3 (2) lim, tanr-sin…

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Q: Evaluate the limits with either L'Hopital's Rule or previously learned methods: 1-cos x 4. lim x2

A: We need to find the limit limx→0 1-cosxx2. So,             limx→ 01-cosxx2By L'Hopital rule,=limx→…

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: 2. Use L'Hopital's rule to find the limit; * - sin (*)= lim メ.Sin メーラ0

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Q: Only one of these calculations is correct to evaluate the definite integral Inx dx Select one: Inx…

A: Integral test:  Integrals convergent if the associated limit exists and is a finite number (i.e.…

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

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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: Identify the limit that represents the limit definition of the definite integral ∫39 6x3 dx using a…

A: From the given indefinite integral, observe that f (x) = 6x^3, the lower limit and upper limit is 3…

Q: Evaluate the definite integral by the limit definition.

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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: evaulate the definate integral by limit definition

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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: If the Midpoint Rule is used on the interval [-1, 11] with n = 3 subintervals, at what x-coordinates…

A: Consider the interval a,b=-1,11n=3. The length of interval, ∆x=11+13=4 Class intervals…

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: 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. -Дх, [1,4] (x;)2 + 9 lim i = 1 dx

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Q: -x² xe* dx -00

A: Given: ∫-∞∞xe-x2dx

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: Express the limit as a definite integral on the given interval. n x;* lim -ΔΧ, [1, 7] n→∞ dx i=1…

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Q: Prove: the limit as x approaches 0 1-cos(x)/x=0

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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: 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: If f is bounded and integrable in the interval [a, b], (x) cos nx dx3D0. show that lim

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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: cises 1–12 con- of the Integral

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Q: Express the limit as a definite integral on the given interval. cos Xi lim Ax, [3π, 5π] 818 5m 3m dx

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Q: Express the limit as a definite integral on the given interval. lim [9(x;)³ – 9x;14x, [2, 8] i = 1…

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Q: How would I find the limit of the attached equation using L'hopitals Rule?

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Q: Express the limit as a definite integral on the given interval. lim 8x; + (x;)² Ax, [3, 8] dx

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

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

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Q: Let f(x) = ln x / sin^-1 x    analyze the limit : lim x--> 1- (from the left) f(x)

A: Given information:The given function is

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: limit x approaches zero, sin^2x/x

A: Given,

Q: What is the limit as x approaches 0 of 2x/sin(x)

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.