Let xn -> 0 and (yn) be bounded. Prove xnyn -> 0.

Q: Find upper bounds for the error in approximating the integral 1/(6+x) bounded by [1,-2] by the…

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Q: Sketch a continuous function ƒ that is positive over the interval [0, 1) and negative over the…

A: Given that f(x) is posotive over [0,1) and negative over (1,2] And the area bounded by f(x) and…

Q: Use the definition of the definite integral as a limit of a sum to evaluate •1 (x2 – 4x – 2) dæ -2

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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: Evaluate the limitlimx→0+x (ln(x))^2

A: To determine the value of the limit.

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: Express the limit as a definite integral on the given interval. in lim [5(x,")3 – 2x,*]Ax, [2, 7] i…

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

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Q: Estimate the area under the graph of f(x)=1/x+3 over the interval [-1,2] using ten approximating…

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Q: Express dx as a limit of left Riemann sums but do not attempt to eval- x2 uate the limit.

A: Given, ∫-11-6 5x2dx

Q: By using the limit comparison test, the integral

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Q: How are the continuous extensions often found?

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Q: Describe a case where f(x) has a limit but is not continuous?

A: We know, if the left-hand limit is equal to the right-hand limit, then the limit of the function…

Q: Express the limit as an integral. * lim (5(x)2 - 2(x;)³)Ax over [0, 3] i = 1 dx

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Q: use the limit of the Riemann Sum to find exacct area under the curve. fCx) = 4 x [2,5]

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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: Compute the limit as x approaches infinity of x^e-x

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Q: Estimate the area under the graph of f(x) = x° between x = 0 and x = 4 using each finite…

A: Given,  f(x)=x3 and a=0 and b=4

Q: Find the area bounded by f(x)=10−4x2 and the x-axis on the interval [1,2] by finding the limit of…

A: Given that Here a = 1 and b = 2 Find expression of the lower height

Q: Find the limit. lin x->∞ arctan(ex)

A: Given: limx→∞tan-1ex for evaluating this limit have to use  limx→∞ex=∞

Q: Express the limit as a definite integral.

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Q: Express the limit as a definite integral. lim xk Ax [-3, 2] 4-0 k 1

A: Given

Q: Evaluate the definite integral: x²)dx using limit of the Riemann sum.

A: Consider the provided definite integral, ∫02 2-x2dx Evaluate the provided integration using limit of…

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

A: limn→∞∑i=1nxi*xi*2+4∆x,    1, 9 Here, fx=xx2+4, a, b=1, 9

Q: Estimate the area under the graph of f(x) = 2x between x= 0 and x = 8 using each finite…

A: Width of the interval [0,8] is (8-0)=8For two subintervals , width of each interval=82=4So the…

Q: limit

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

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Q: evaulate the definate integral by limit definition

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Q: Estimate the area under the graph f(x) = x2 between x = 0 and x = 2 using left sum with two…

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Q: 3 tion of 129.9 cm. Use the given stand= ify the limits separating values that are

A: Given:Mean=x¯=1118.8 cm3Standard deviation=s=129.9 cm3Sample size=n=20 According to the Range rule…

Q: Find the limit of xsinx as x approaches 0

A: Given:

Q: Estimate the area under the graph of f(x) = x° between x = 0 and x= 4 using each finite…

A: Given: f(x)=x3   between x=0 and x-4

Q: Use L' Hopital's Rule to find the limit as x approaches zero of:  (1+2x)^(-3/x)

A: Here, we will find the limit of the given expression by using  L' Hopital's Rule. The expression is,…

Q: Use a finite sum to estimate the area under the curve using the midpoint rule f(x)=x^3 on the…

A: Width of the interval [0,2] is = 2-0=2So for two rectangles the width of the subintervals=∆x=22=1So…

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

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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: 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: 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: Find the limit if it exist if it does not exist right DNE limit X to zeros in 2x/4x

A: This question can be solved using the concept of limits.

Q: find it's average value over the interval f(x)=-6x^2-3 on [0,2]

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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

A: Question: Answer:

Q: Determine if the improper integral converges and if so, find the value it converges to. Use…

A: Given Data: Integral: ∫1∞1xxdx Using integral test, Rewrite the integral. ∫1∞1xxdx=∫1∞1x32dx

Q: Express the limit as an integral. Š (5(x; )² – 3(x; )³)ax over [0, 2] lim

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Q: Use the Midpoint Rule to estimate the integral. n=4

A: Since we have been given up the integral ∫191xdxOur aim is to estimate the integral till n=4 using…

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

A: Let's find.