Using L'Hopital's rule, calculate the following limit: T-sin r lim, 0 O 1/6 O 1 O does not exist

Q: Evaluate the integrals in the following questions using integration by parts for SincE In (x + x²)…

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Q: 23 Given the ordered pair P, determine the requested sin, cos, or tan of angle . P(5,5) tan0 =…

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Q: 3. 4x 3 + dx

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Q: įsin' | sin' xdx The integral of is

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Q: 20 The slope of the function ƒ(x) = 5x - 5 is ______. 1 -5 5 -1

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Q: x = -3 is a critical number of the function f(x) = (x – 3)(x + 3)². Select one: O True O False

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Q: Evaluate

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Q: The series 7 n3+ 9 n=1 6 n+ 1 is divergent. Select one: O True O False

A: Given query is to find that statement is true or false.

Q: •1//2 4 c) dx. VI – x² 1/2

A: To evaluate the integral.

Q: a) [ Explain why the following series * (-1)" 00 Σ 1 + n5/2 n=1 is Alternating. b) ! : Use the…

A: Solve the following

Q: The functions h(x) and h'(x) are not differentiable at x = 0. The graph of h has a point of…

A: Follow the procedure given below.

Q: 1- v extends from (0,0) to (-3,2). Vector W extends from (0,0) to (-3,5). a- Find the magnitude of V…

A: This is a problem related to vector. Based on the general formula and concepts we will answer the…

Q: Find the minimum and maximum values of the function y = 8Vx² + 1 – 7x on the interval [0, 8] by…

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Q: -olve for two cases csc² 20 cot 20 de irst case Using u = cot 20

A: Topic:-  integration

Q: dy - 3y = 0 dx 16. Solve the first order linear differential equation: А. y = e* + C В. у3 Сезх C. y…

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Q: Bacteria are reproducing in concentric rings in a petri dish. The circular area occupied by the…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

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Q: A curve is defined implicitly by the equation ax + by2=r2 Given that a=20, b=2 and r=7, find the…

A: We have to find the solution.

Q: 12. S cosh(5x – 7) dx

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Write each of the other trigonometric functions of e in terms of cos(e). (Enter your answers as…

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Q: Plane travels for 9.5 hours on two-way trip between location A and B. The Plane can fly at 320 km/h…

A: Plane travels for 9.5 hours on two-way trip between location A and B. The Plane can fly at 320 km/h…

Q: 2t dt 8. (1²+2)°

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Q: Let f(x) = 2^x+ x. Find (f ^−1)′(1).

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Q: dy Do not simplify your answers. dx IV. Find Vsec-1r sin æ 1. y = (use logarithmic differentiation)…

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Q: A hot air balloon rising vertically is tracked by an observer located 5 km from the lift-off point.…

A: Given: x=5 km θ=π5 raddθdt=0.3 rad/min The person and the hot air balloon form a right triangle,…

Q: II. Determine if Vx2 – 3x – 4, if x 1. is continuous or not at x = -1 and at x = 1. In the case of…

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Q: Find !V1-cos xdx 2 sin x = 1- COS X V2(-cos x/2)+ c 1/ /2(-cos x/2)+ c В. 2/2(-cos x/2)+ c С.…

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Q: Find the critical points, relative extrema, and saddle points of the function. (If an answer does…

A: f(x,y)=x2+y2+6x-2y+6

Q: Question 2 [ a) [ : Explain why the following series (-1)" Σ 1 + n5/2 n=1 is Alternating. b) h. 1:…

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Q: Q: Solve the following D.Eqs. (Use undetermined coefficient method) 1) y" – 2y' + y = xe* 2) y(4) –…

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Q: Determine whether the function is continuous or discontinuous 5. f(x) =

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Q: Obtain the general solution unless otherwise instructed d²y 1. dx2 - y = 10sin²x

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: The series 33n-54-1-2n is n=1 Select one: а. is convergent but not a geometric series. O b. is…

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Q: Determine the limit: lim 4x2 x→0 sin (2x) cos(2x)

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Q: 5. y = 3x - 4 at (0. - 4)

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Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 63°C, it…

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Q: 1) Use the Integral Test to determine whether the series is convergent or divergent. п (Зп — 1)2 c)…

A: Given problem:-

Q: Evaluate the integrals in the following questions using integration by parts For O cos T0 do

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Q: In (x + x²) dx

A: Given problem:- ∫ ln(x+x2) dx

Q: Evaluate the integrals in the following questions using integration by parts For 0 cos T0 de

A: By Parts Rule: ∫u(x)v(x) dx=u(x)∫v(x)dx-∫du(x)dx∫v(x)dx

Q: Se*(4 + e*) dx Evaluate the integral of A (4 + e*)² + c B. (4 + e*)? +c (4 + e*)² + c (4 + e*)* + d…

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

Q: Suppose a curve is defined by the equation 16(?2+?2)=45.16(x2+y2)=45. Show that if you translate the…

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Q: Use the Integral Test to determine vhether the series converges or diverges. ke -8k k=1 Evaluate the…

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Q: II. Consider the function g defined by 1 g(x, y) = cos (TxVy) + log3(x – y)" Do as indicated. 3. In…

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Q: Evaluate the integral of sinº x dx from o to n/2. А. П/32 В. гп/17 С. зп/32 D. 5n/32

A: We know, 2sin2A=1−cos2A  2cos2A=1+cos2A2cosAcosB=cos(A+B)+cos(A−B)

Q: What is the degree of f (x, y) = 2y + Væ² + y? ? O 1 O 2 O 1/2

A: We can solve as follows

Q: If f(x) is integrable on [a, b] , then f(x) is continuous on [a, b] . O True O False

A: Given statement:If fx is integrable on a,b, then fx is continuous on a,b.We need to check the…

Q: Express the vector 4u + 5w in the form v = v,i+v½j+V3k if u = (3, - 2, 5) and w = (- 4, 5, – 4). 4u…

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Q: Calculate the surface area of the portion of the cylinder X+y 9 that lies betweenz=3 and z=6. O A.…

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Q: Find critical points of the function e(2 -3x) O x = 0, x = 1 O x = 1, x = 3 O x = 0, x = 2 O this…

A: Topic = Derivative