A. Sketch the figure for analysis. Shade the needed region and draw a representative vertical or horizontal dividing lines and border lines. Find the area of the region. x = 4; y? = x

Q: Find the divergence of the vector field F. F(x, y, 2) = In(7x2+ 6y? )i + 42xyj + In(6y2. + 72² )«…

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Q: An unknown function's derivative is h'(x) = 3x-2 - 6. Using your understanding of the derivative…

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Q: 4z² + 5dz 금(122+5) xo 4a? + 5 Part 2 of 2 ewrite the integrand in terms of u so that the integral…

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Q: on. 5x(8- х) dx x(8 - x) dx =

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

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Q: (2) Prove that for any integer L () NTX / sin? dx = L. L -L

A: ∫ cos(ax) dx = 1a sin(ax) +C

Q: Find the derivative of this function

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Q: im Y cosx t Zx メナロ0 7x¢ し

A: Given query is to find the limit of the expression.

Q: Find the moment of inertia of the area bounded by the curve x^2=4y, the line y=1 and the y-axis on…

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Q: d Find [r(t) · u(t)] and [r(t) x u(t)] in two different ways. dt dt r(t) = ti + 2t2j + t³k, u(t) =…

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Q: nd the S (1–) dx A. x– 2 In|x| – +c B. 3x – 2 In|x| –-÷+c C. 2x – In|x| –+c D. x– In|x| - +c

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

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Q: Evaluate (z° + 6) dæ (z³+6)® +c А. 18 (z³+6)° В. +c (x³+6)* 16 С. z18 + 2x15 + c

A: topic - indefinite integral

Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

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Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

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Q: 14th term of the following geomnetric sequence. Find the 1. 2, 4, 8, 0. 昌 唱

A: Use geometric series concept

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: +y = e=* sin x

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Q: y = sin3x

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Q: Find the accumulated amount if AED 6,000 is deposited at 2.5% compounded semi-annually for 5 years.…

A: Given query is to find the amount accumulated.

Q: Let ABCDEF is a regular hexagon with centre O. Let ā = 0A, b= OB and so on. Explain why/prove %3D…

A: We know that in an regular hexagon the distance from center to any vertex is same, then the…

Q: Find the J(2x + 1)³ dx

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Q: x² + 4x + 1 dx (x – 1)(x + 1)(x + 3) d* - Inlx- 1+Inlx+11- n|r+ 3| +C Inlx- 11+Inlx+1| +Inx + 31 +C…

A: Let's find.

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: Find the 22 term of the arithmetic sequence whose common difference is d=4 and whose first term is…

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Q: 9. A triangle has two sides represented by vectors OA = (2,-3) and OB = (3,1). Determine the…

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Q: Approximate the point of intersection of the graphs of fand g. Then solve the equation f(x)=g(x)…

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Q: Verify Green's Theorem by evaluating both integrals ON aM | y? dx + -x² dy dA ax ay for the given…

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Q: Verify Green's Theorem by evaluating both integrals aN aM dy dA ду ax for the given path. C: square…

A: Application of integration

Q: 8. Relationship Between Continuity and Differentiability: (a) Justification needed): If lim…

A: To discuss the  relationship between continuity and differentiability.

Q: Describe the graph of the equation. r= 5 cos t i - 18 sin 1 j +k O An ellipse in the planex = 1,…

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Q: A small resort is situated on an island that lies exactly 4 miles from PP, the nearest point to the…

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Q: 1. Find the particular solution of the differential equation that satisfies the initial conditions.…

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: I have stated the used formula in the solution

Q: ||r'(t) x r"(t)|| Use the formula k(t) : to find k(t). 3 r(t) = ei+etj K(t)

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Q: uences below are either arithmetic sequences or geometric seguences. For each sequence, determine…

A: Given query is to find the type of the sequence.

Q: Prove the given identities. csc 0 – cot 0 (a) sec 0 – 1 = cot 0 (b) cot 0 + tan 0 = csc 0 sec 0 For…

A: a) [csc(theta)-cot(theta)]/[sec(theta)-1]=cot(theta) b) cot(theta)+tan(theta)=csc(theta)sec(theta)…

Q: On the axis below, sketch the graph of a function, f, which has a critical point at r = 1 4. (.. but…

A: Solved below

Q: 7. a) Find the indefinite integral. (Remember to use absolute values where appropriate) 1 dx 4x -

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Q: 6. Find the indefinite integral. S 3x³ V3x4 + 7 dx (Use substitution method)

A: Solving the problem by finding the value of integration.

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. 2(3*)…

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Q: Find the divergence of the vector field F. F(x, Y, z) = In( 9x²+ 8y² )i + 72xyj + In(8y² + 7z? )«…

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Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

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

Q: lim (3x + 1) sin(2x) 4x2

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Q: 13. Find the length of the curve y4 + 8 from y = 1 to y = 4. X = 4y2

A: To find the length of given curve.

Q: 2Tan 'x - x 9. lim,0 'x0 2x – Sin 'x

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Q: As you will show, exponential growth functions ekx always dominate power functions x", and power…

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Q: Find the vector equation for the line of intersection of the planes x – 5y + 2z = 1 and æ + z = 1 |…

A: To find the vector equation of the line of intersection of given planes.

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

A: Here we have r(t)=t2i+t5j We have to find κ(t)=r'(t)×r''(t)r'(t)3 ..................................…

Q: Consider the matrix -8 A = 13 21 1 4 -2 15, Where a;, represents the entries for A, for i= 1,2,3 and…

A: Given,        -8    0    5 A= 13    21  1         4    -2   15 a ij represents the entries for A,…