Use L' Hopital's Rule to find the limit as x approaches positive infinity of:  x/(e^x) Have a good day!

Q: Use the definition of the definite integral as the limit of a sum to evaluate (4x

A: Definition of Definite integral  The definite integral of a real-valued function f(x) with respect…

Q: Express the limit as a definite integral on the giveninterval.

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Q: 2 dx 2-x

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Q: Estimate the value of the limit to 3 decimal places.  limit as x appraches -1 of 1 plus x to the…

A: The given limit is, limx→-11+x31+x13. Note that, the given limit is in the indeterminate form. Apply…

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. [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: Evaluate the integral. S tan (2x) sec (2x) dx .5 Find the limit

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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: By using the limit comparison test, the integral

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

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

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Q: Express the limit lim ! as a definite integral. Evaluate the definite integral. nil+(:)

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Q: Compute the derivative of h(x) = 3x – 5 using the limit definition (do not use L'hopital's rule).

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Q: Express the limit as a definite integral.

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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 giveninterval.

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Q: Evaluate the definite integral by the limit definition.

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Q: Find the limit of the following functions by using L’Hopital's Rule. (i) lim ( cosec x

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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: 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 n- 00 [4(x;)³ – 4x;"]ax, [(2, 7]…

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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: 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: V1+ sin t dt lim

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Q: -x² xe* dx -00

A: Given: ∫-∞∞xe-x2dx

Q: Evaluate the integral below or state that it diverges. Use proper limit notation dr 4.

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Q: (In 0 lim 0 → sin 0 cos 0

A: Given limθ→πlnθ-lnπsinθcosθ

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: 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: See image below.

A: To find: -

Q: Express the limit as a definite integral on the given interval. n exi lim -Ax [0, 9] n→∞ i = 1 6 +…

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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: Find the following limit using l'Hopital's Rule: Lo Vi cost dt lim x→0+ x2

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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: Express the limit as a definite integral on the given interval. lim x, In(2 + x^)Ax, [3, 4] n- 00

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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: Use the definition of the definite integral as the limit of the Riemann sum to find

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

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Q: Express the integral ° (1 + 2x³) dx as a the infınite limit of Right Hand Riemann Sums.

A: ∫abfxdx=∫161+2x3dx where a=1, b=6

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: (sec 0 – 1) lim 02

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Q: Give the definition of the definite integral as a limit using the right endpoint approximation.

A: Let's find.

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.