5. Use L'Hospital's rule to compute the following limits (a) lim a In(x) (b) lim sin(z) (c) lim 15t-401² – 1 10-t-8t3 t+1

Q: 1 (5* )csch- if y= (e oshS ) In Vx² +1 2 a) Find dx dy x+1 x>0. 2 x++1

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Q: 10. * -1 x CSc

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 8 y + 3 = z +…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: Given problem:- Use Lagrange multipliers to find the maximum and minimum values of f subject to the…

Q: Consider the following planes. 3x + 4y - z = 28 x - 8y + 2z = 0 (a) Find the angle between the two…

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Q: Kindly write the step by step solution. Two particles, A and Bare in motion in the xy-plane.…

A: Two particles,A and Bare in motion in the xy-plane.Their coordinates at each instant of time t…

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

Q: Answer the following about the function F(x)=x^4-24x^2+700. Justify all your answers. A. Find the…

A: Given

Q: 1. In the following exercises, evaluate each definite integral using the Fundamental Theorem of…

A: a) ∫-12x2-3xdx=x33-3x22-12=233-3(2)22-(-1)33-3(-1)22=83-6+13+32=-32∫-12(x2-3x)dx=-32b)…

Q: 9-1 -dy

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Q: x = -4 + t, y = 2t, z = 7 + t (a) (0, 8, 11) O Yes O No (b) (4, 5, 9) O Yes O No (c) (-6, -4, 5) O…

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Q: Use a trigonometric identity to find cot ( - x) if tan (x) = 8. (Express numbers in exact form. Use…

A: Topic = Trigonometry

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-8,-6)…

A: Let's find.

Q: Example 2.35: Using Implicit Differentiation to Find a Second Derivative d'y dx Find if x +y² = 25.

A: Explanation of the answer is as follows

Q: Find dx (1 – x²)³/2 + c Vx2 – 1 V1 – x2 Option 3 Option 2 Vx2 – 1 + c V1- x² - Option 4 Option 1

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Q: .f (x) = cos(-x) .f(x) = sin(8x) .f (x) = 2 sin(-5x) a) f'(x) = 2 sec(2x – 1) tan(2x – 1) %3D - b)…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: Yes,  you did not say what a is and what b is. Their values

A: Apologies for the inconvenience.   To find a and b we set the equations equal to each other and…

Q: 1. Given: - Ar with f'(x): (x+ 2)2 r(x + 8)(x – 2) (r +2)3 8(7x-4) (r +2)4 S(x) = and f"(x) = a.…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Answer the following about the function F(x)=x^4-24x^2+700. Justify all your answers. A. Find all…

A:

Q: Dis bounded by the planes y 0, y 2,x=1, z=0 and z =(3-x)/2. Evaluate the triple integral with order…

A: Given Dis bounded by the planes z=3-x2,y=0,y=2,z=0 and x=1

Q: Solve the exponential equation by taking the logarithm of both sides. Express your answer in exact…

A: Given

Q: Match the answers to its antiderivative. Antiderivative Answer A. J kda In(z) + C II. B. ['dr + C…

A: As we know that; The Power rule; ∫ax+bndx=ax+bn+1an+1+C ; n≠-1 And ∫eax+bdx=1aeax+b+C…

Q: 86 10. 24 abe 2:4:3 9.

A: Answer 9 but given information in question 10 is incorrect

Q: Determine the interval(s) on which the function is continuous: 2r+ 7 212-3x-9 if x 1/2 Ox1/2 Ox1/2…

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Q: Solve the following differential equations using the method of undetermined coefficients. y" – 3y" +…

A: This is a problem related to second order differential equation. Solution will be conjunction of…

Q: Find two unit vectors in 2-space that make an angle of 45° with 7i+ 6j. NOTE: Enter the exact…

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Q: sin x 34. lim 1 - x o0-r

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Q: State whether the following numbers are rational or irrational. a) V4+7/2 b) V36 c) V112510716

A: Given: a)4+72b)236c)112510716

Q: Finding Vertical Asymptotes In Exercises 63–68, find any vertical asymptotes of the graph of the…

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Q: Choose the correct answer. 1. The sequence (x) = (-n) is. a) Cauchy b) bounded e) divergent d)…

A: We have1) The sequence (xn)=(-n) is . . . . . . . . .Now we have take n=1 x1=-1put n=2x2=(-2) So, we…

Q: 1 Suppose that L is a location function of an object, given as L(t) = We will compute the 3t – 2…

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Q: 2 sin? x 7. lim x→0 5x(1+cos x)

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Q: B) By using (A), Find lim /-

A: limn→∞1n

Q: (0³+ 38+ 3D+ 1)y-8sinx ylo): -/ y'l0)= 3 y"16)=5 5-

A:

Q: A farmer's house sits 3 miles due south of a river. The diagram below shows the path that the farmer…

A: First assume a distance as x then make the relation between total  distance  and x.. And then for…

Q: Find the angle 0 between the vectors in radians and in degrees. - co) + sin() = cos 4 u = cos i +…

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Q: O Find all velues of sx for whEu tue serics Converjes. for these alues of l, wnte tue sum of tue…

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Q: Consider the equation x^3=1-2x, which has a unique root between x=0 and x=1. Apply Newton's method…

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Q: Referring to the graph above, which of the following statements is correct: 1. f″(x) 0 for all x

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Q: Solve the differential equation by variation of parameters. 2y" — 4y' + 4у %3D е* sec x y(x) = %3D

A: Solution is given below:

Q: Solve the differential equation by variation of parameters. y" + 3y' + 2y = cos(e*) y(x) =

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Q: endicular to the plane z + 3y – x = 7 and containing the points (2, 5, 0) and (0, 2, -1)

A: Here we have to find the equation of plane which is perpendicular to the other plane.

Q: xdx + ydy == (x² + y²)dx

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Q: Explain why S is not a basis for R2. S= {(3, 5), (1, 0), (0, 1)} O sis linearly dependent. O does…

A: The given set S=3,5, 1,0, 0,1

Q: In x 35. lim

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Q: 3. Find the Volu me oF the (olid generated by revoluin g ab out the y-axis the region bounded the…

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Q: 1. Given: 7- 4r S(x) (z+2)² ' with f'(x) = (z + 8)(z= 2) and f"(z) = 8(7x – 4) (x+2)³ (z+ 2)* * e.…

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Q: АCTIVITY GIVEN : 2x 2x 1 2х + 3 1 f (x) = 1 –x 8 g(x) = 3(x + + 4 h(x) = 6 a.lim -4 · f (x) d.lim (8…

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Q: Determine whether each of the following statements is True (a) For a quadratic function f(x) - b x^2…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: To use Lagrange multipliers to find the maximum and minimum values of f subject to the given…