31.| CSC I COLI dt

Q: Evaluate the line integral / (3x + 9y)dx + (4x – 5y)dy along the curve C : x = 10 cos t, y = 20 sin…

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Q: Evaluate r(g(t)) using the Chain Rule: r(t) = (e', e*, -6), g(t) = 5t + 6 %3| 을r(g(t)) = 《

A: Use chain rule

Q: Solve the equation for x and y x+v=300 5x+8y=2100

A: Given query is to find the solution of the system of equations

Q: Question8: Choose one answer. You decide to collect a bunch of cans of soda and measure the volume…

A: To solve the following problem

Q: Given h(r) = 1/r+3 find the following: (a)h(x2)= (b) h(x2 + 1)= (c)h(x2) + 1=

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Q: P(x) Let P(x) and Q (x) be polynomials with the degree of Q (x) greater than the degree of P (x) and…

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

A: To discuss the  relationship between continuity and differentiability.

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

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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: 6. Vectors i and v are positioned at 115° to each other such that lü| = 15 and l0| = 7. Determine…

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Q: 2X メ→チ 7-x

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Q: Given the curve v = x3 – 3x find the stationary or turning point

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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: 2x2 +4x - て +2

A: To evaluate the given integral.∫2x2+4x-3x2 dx

Q: 2. True or False? a) -2(3BA)and 6AB'are equal vectors. Justify your answer. b) If |AB| = |AC|, then…

A: This question can be solved using the concept of equal vectors.

Q: In the year 2000, the population of a small city was 43,000. The population grows at a rate of r(t)…

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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: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: Improper integral: If f(x) is not continuous at x=c where a<c<b and ∫ac f(x) dx and ∫cb f(x)…

Q: Use the Comparison or the Limit Comparison test to show convergence or divergence of each series.

A: Explained below

Q: mparison test to determine whether the given series conve:

A: Please refer to the image below

Q: Use shells to find the volume of the solid obtained by rotating the region bounded by y = H= 1, and…

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Q: Evaluate the line integral / (x +8y)dx + (5x – 4y)dy along the - curve C : x = 8 cos t, y = 16 sin t…

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Q: (9, -7) (3, 1). Find 吕 ロ师仁 ?

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Q: Find the constants a and b such that the function is continuous on the entire real line. x 5

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

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Q: Find div F and curl F if F(x, y, z) = x°i – 2j + yzk. div F= curl F=

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Q: dy Solye the differential equation 3a2y = = -y, s.t. y (0) :

A: Topic = Differential equation

Q: 7. -4 3. ) dx - 3 10.

A: The given integral,         ∫e5xe2x7+3e3xdx

Q: E. Find the point of intersection of the plane 2x+3y+z 5 and the line x- 3 y+4 z- 1 1 II

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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: e2x - e 2x 3. lim, 0 sinx

A: To evaluate the given limit.limx→0 e2x-e-2xsin x

Q: The sixth term of a geometric sequence is 1215 and the third term is 45. Find the first term and the…

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Q: Find div F and curl F if F(x, y, z) = 3e*"i – cos yj+ 7sin? z k. %3D div F= curl F=

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Q: In(1+x) -x cosx -1 1. lim x-+0 7- In(2x + 3) 3. lim x-00 In(5x -2)

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

Q: E(-1)n+1_2 Vn n=1

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Q: 22. The power series £4, (x – 3)" converges at x = 5. Which of the following must be true? n=0 (A)…

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Q: Inx Evaluate the limit using L'Hospital's rule: Lima0 cosh

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

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Q: Find V × (V × F) if F(x, y, z) = 6xyj+ 4xyz k. V x (V × F

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Q: Find the volume of the solid generated by revolving the region R bounded by the graphs of the given…

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Q: Verify Green's Theorem by evaluating both integrals aN dx + x² dy = / / dA ay y2 ax for the given…

A: To verify green's theorem by evaluating both the integrals.

Q: Write the expression as a single Integral 1. f f(x)dx + f(x)dx =, 2. S f(x)dx – , f(x)dx = 3. f…

A: Use the property of the definite integral; 1). ∫abfxdx=-∫bafxdx 2). ∫acfxdx=∫abfxdx+∫bcfxdx   1).…

Q: Find V. (V × F), if F(x, y, z) = e²i+ 3xe"j – 7ev*k. - V · (V × F)

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Q: x-4 dx x2+2x-15 1 -In]x + 5 - Inlx - 31 +C 9 In|x +5|- In|x – 3| + C Option 1 Option 2 Ln x + 5)이 1…

A: Given problem:-

Q: Find the Laplace Transform of the following functions: a. L(sinxcosxe*} b. L{

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Q: +y = e=* sin x

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Q: Sketch a single graph of a function f(x) which satisfies all of the following the limits and values.…

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Q: Find the interval and the radius of convergence for the series n=1 n2"

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Q: Find V × (V × F) if F(x, y, z) = 4xyj+2xyz k. V × (V × F) :

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Q: Consider the function f(x) = 1/3x3 + 3/2x2 - 4x. At which point(s) is the slope of the tangent line…

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