1 Without a table of values and using index laws, sketch y 2*-

Q: Find curl (8z i + 9x j+ 6y k). curl (8z i+ 9x j+ 6y k) = ( )i + ( i j + ( i )k

A: Find curl

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. p…

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Q: Find the curvature and the radius of curvature at the stated point. Edit r(t) = 8 cos(t)i+ 7 sin(t)j…

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Q: Find div F and curl F if F(x, y, z) = 8y°z³i – 11x*z°j – 3xy°k.

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Q: Find the particular solution of the DE y " -11y + 24y = 0 subject to the boundary conditions y (0) =…

A: Given y''-11y'+24y=0  ; y(0)=2  and  y'(0)=-3

Q: 2. lim (ex – 1)lnx X0+

A: (2). The given limit is: limx→0+ex-1lnx As we know that, the second indeterminate form is: ±∞±∞ ;…

Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = e"i+ e*j к(t)

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Q: Find the partial derivative. 17zy

A: Given, ∂xe17xy∂x We have to find the partial derivative.

Q: 6. lim (sinx)* X0+

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Q: 3 d : 4me-m2 dy. dm

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Q: Find curl (7z i + 8x j + 9y k). curl(7z i + 8x j + 9y k) = ( i )i + ( i )j + ( i )k

A: This question is related to vectors, we will solve it using given information.

Q: Using the fundamental theorem of calculus, find the derivative of the integral -3x+2 t -dx 1+t3

A: We have to find derivative of given function.

Q: How many arbitrary constants will be there n the general solution of a second order differential…

A: The number of arbitrary constants in the general solution of a differential equation is equal to the…

Q: Evaluate the line integral -ydr + rdy along the curve C : y² = 6x from (6, 6) to (0,0). NOTE: Enter…

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Q: Solve d 4me-m2 dy dm

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Q: Find the radius of convergence, R, of the series. xn + 1 3n! n = 2 R = Find the interval, I, of…

A: A detailed solution is given below.

Q: If the function f(x) is continuous in the interval [-7.0] and f(-7) = 32 and f (0) = –1, then which…

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Q: e2y dy Solve using algebraic substitution Tey-i

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Q: Which integral corresponds to the area of the shaded region between the curves y = |a² – 4| and y =…

A: To find the area of the shaded region.

Q: 1.) Find the area bounded by the curve y?= 1 - x and 2y = x + 2 2.) Find the area bounded by the…

A: Solution is given below:

Q: Evaluate the integral / (8x + 18y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A: We have to find value of given Integral along given Curve.

Q: 1.) ° 6x3+4x²-8x dx I. Evaluate the following Definite Integral. 1.) ° 6x³+4x²-8x 2.) x²(2x3 + 1)Fdx…

A: we want to find the integral ∫03( 3x-6 -1 )  dx

Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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Q: Evaluate the double integral. 7x sin y'dA; Ris the region that is bounded by y = x², y = -x', and y…

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Q: Without evaluating the constants, the partial fraction decomposition of 7x3 – 11 (4x3 + 7x2 +…

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Q: A lighthouse is on an island 250 meters off shore. The lighthouse beam makes a full turn every 7…

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Q: A general solution of the differential equation - 3+4 = 0 is 1. A. y = c,e* +cze2x + c3xe²x B. y =…

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Q: Find curl (2z i + 3x j + 5y k). curl (2z i + 3x j + 5y k) (i )i + ( i j+ ( i )k

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Q: Use the Table of Laplace Transform to find the Laplace Transform of the given function. a. te-3t b.…

A: As per our guideline, we are supposed to answer the only first question with 3 subparts to get the…

Q: )Solve for k such that 1 k(x2 – 2x + 1)dx = 5 - 0.

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Q: Exercises: Imaginary Roots of Auxiliary Equations Solve the equations 1) (D2 – 2D + 5)y = 0 %3D 2)…

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Q: Q1: Find the length of a and b in the following triangle a 75 30

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Q: I. Evaluate the following Definite Integral. 1.) L,9 6x3+4x2-8x dx 2.) x²(2x³ + 1) dx 2x 3.) sž…

A: Integration

Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 5xyz k. V × (V × F) :

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Q: A company is planning to manufacture snowboards. The fixed costs are $400 per day and total costs…

A: Cost

Q: II. Find the Inverse Laplace of the following 1 a. s² +6s+25 s2 b. (s-1)3 7 C. s4 8 - - - s3 s2

A: According to bartleby guidelines when student post multiple subpart questions then expert must have…

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

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Q: 3. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1…

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Q: Find the particular solution of the DE y''-11y'+24y=0 when y(0)=2 y'(0)=-3

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Q: dy For each of the following functions determine dr

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Q: The area enclosed by the curves y = x + 2 and x is . y = 7 + 5x %3D - .... 1) 36 2) 120 3) 34 4) 118…

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Q: Find the general solution 5. (D² – 1)y = 0

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Q: dx 2. Find the integral x²(x+1) In (***) + C b. In (***) - +C 1+ C c. In (***) ++ c d. None of the…

A: Here we have to find the integral

Q: Find the area bounded by the indicated curves. y = (x - 1)2, y = 8x - 24, where 3 s x s 5 Optional…

A: Let us draw the graph.

Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = e*i+e*j ,3t: K(t) =

A:

Q: 2. SET-UP the definite integral that will give the area of the region specified using (a) x as the…

A: Area

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* r(t) = 8 cos(8t)i+ 8 sin(8t)j + 5tk…

A:

Q: Describe the graph of the equation. r= (5 - 31) i - 10:j O tis a line in 2-space that goes through…

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

Q: dz 14. Evaluate S z(4+2)

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Q: (-1)r+1. n=1 と(-1)"+1 n2 2]

A: Topic:- sequence and series