34 Count lim (1+x) F b) lim (1-x)* メ→0 The limit in (a) determines e. What special number does the limit in (b) ?

Q: A spring has a natural length of 22in. A force of 16001b stretches the spring to 32 in. How far…

A: We will use rules of spring stretch to solve it.

Q: (a) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) =…

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Q: 2. Use the Divergence Theorem to compute ffs F. dS for F = (xy, yz, x² z + z² ) and S the boundary…

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Q: dy If y = tan? x, find da

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Q: Given the force field F, find the work required to move an object on the given orientated curve. F =…

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Q: |r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = ei + etj 30 е4 K(t) : e-t (25 el2t + 1)

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Q: 5. Use the Second Fundamental Theorem of Calculus to find F'(x). х 1 F(x) = S* dt.

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Q: п! n4 n=1

A: The given series is: ∑n=1∞n!n4 Let, an=n!n4; n≥1

Q: Find all the critical points of the function f(x, y) = x³ + y³ – 9x2 – 21x – y - 66 and label them…

A: Local Extremum values:              Consider the function f(x,y) .For critical points , fx(x,y)=0…

Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x? b.…

A: area under the curve

Q: Consider the following statements. 1-If B is a symmetric matrix of 9x9 so the elements b32 and bz3…

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Q: Product A and Product B are two different items manufactured by the same firm. Product A is…

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Q: Solve the equation algebraically. Round the result to three decimal places. 3+ln x = 0 8 e-354.598…

A: Using algebra

Q: 8 f(x, y) = y/x, P(1,2), u = }(2i + 5 j) |(2i + /5 j)

A: To find the gradient at the given point and then rate of change for the given function.

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: x-axis from x = 0 to x = 4

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Q: Determine the value of t that maximizes the area above the x-axis and below the graph of the…

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Q: (a) Alina needs to make a flyer for her band's concert. The flyer must contain 20 square inches of…

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: 2ln|x| + 3 ln|x + 1| – * - + C 5x2+11x+2 dx x(x+1)2 2ln|x| + 3 In|x + 1| ++C 4 2ln|x| + 3 ln|x + 1|…

A: Given: I=∫5x2+11x+2xx+12dx   As we know that; The Power rule; ∫ax+bndx=ax+bn+1an+1+C And…

Q: AX = B is a matrixial representation of a lineal system of equations. Over the augmented matrix (…

A: Here we have to choose the correct option.

Q: f(b) - fla)

A: We have to choose the correct option from the given options according to the given information

Q: Consider the piecewise-defined function Jr+3, |1- x, x 0. (a) FUNCTION, so it must pass the…

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Q: 3. -2 -1 5. Find the velocity, acceleration, and speed of a particle traveling along the curve…

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Q: Use a change of variables (Substitution Method) to evaluate the following definite integral. Show…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 3…

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Q: Find V x (V × F) if F(x, y, z) = 8xyj+7xyz k. V × (V × F) =

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Q: R be the region bounded by the curves y = 10 − x^2 and y = x^2 − 8x. Set up, but do not evaluate,…

A: Given query is to setup the integral for area .

Q: What is the amplitude of the function y=f(x)= 2sin A) 3 в 5 c) 2 D) 7

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Q: the

A: We will find the derivative.

Q: on. 5x(8- х) dx x(8 - x) dx =

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Q: Dest. 3. Supply Sources! 6. 3. 10 7. 20 3. 10 11 15 30 Demand 15. 17 28 Find the initial solution…

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Q: Ex: Investigate the convergence of the following series. H.W 1 7 2) ΣΥ-1 3n 2n+5n IL !

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Q: Determine the amplitude, period, midline, and phase shifts of the function. Then write the equation…

A: Given problem:- Determine the amplitude, period, midline, and phase shifts of the function. Then…

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: To find the volume of the given solid using triple integral.

Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

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Q: 5 Sine cose do 1. Sine+ 3sine - 4

A: Indefinite integral

Q: [2.xyy' – y² +, Vy* +x* ; 4– %3D

A: ∫x2+a2 dx = xx2+a22+a22lnx+x2+a2+C

Q: The answer above is NOT correct. Use calculus to find the volume of a cap of a sphere with height h…

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Q: 102: Find div F and curl F if F(x, y, z) = xz°i+ 5y1ºx²j+4z²yk. div F = curl F=

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Q: y+1 - Z 4. Find the distance between the lines = z and x = 3 %3D -2

A: topic- distance between lines

Q: 2" 5n+1 n=1

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Q: у" — у' — бу %3D2, у (0) %3D 0, y'(0) = 0

A: Given can be written as (D2-D-6)y=2 The general solution will be y=CF+PI Complementary Factor(CF):…

Q: Evaluate the line integral / (9x + 10y)dx + (5x – 6y)dy along the curve C : a = 6 cos t, y = 12 sint…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 7 cos(t)i + 3 sin(t)j+…

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Q: Find curl (3z i + 4x j + 6y k). curl (3z i + 4x j + 6y k) = ( i )i + ( i )j + ( i )k

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Q: Solve the inequality involving absolute value. |x-3|/4<2

A: Given :        x-34&lt;2

Q: For the given position vectors r(t), compute the (tangent) velocity vector r'(t) for the given value…

A: Find derivative of position vector then we get velocity vector then put the given value

Q: CoS X F 2x 7x

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

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Q: 7. 1 (x dy – y dx) = 0 %3D x² + y²

A: Here, the given DE is: 1x2+y2(x dy -y dx)=0...(1)

Q: 4. (x³ + 3x – 1) dx 2 5. 4x x2 6. SIy + 1) – (y? - 1)]dy

A: