Let F(x, y, z) = x³i+y³j+z³k. Compute the following: (i) V.F (ii) V X F

Q: Solve the given Homogenous DE 1) y (ax-2y)dx -x (6x-y) dy=0 when x = 1, y=1

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Q: 1. Determine the type of conic section that each general equation will produce. Show your solution.…

A: As per the rules, we are supposed to answer the first question and rest can be reposted.

Q: 1. Find the derivatives of the following functions: a) f(x) = 2x³ + e²x b) f(x) = ln (2x - 1)5

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Q: * 36, got 6=-8, 311/2<0² 2π1₁ eSC

A: given cot(∅)=-8tan(∅)=1cot(∅)=-18∅=tan-1-18∅=352.8749837o

Q: Consider the system below. y = kx2 y' = k'x2 + 2xv y" = k"x2 + 4xv' + 2v Now, find y' and y"…

A: We need to find y' and y''

Q: (c) Find the value of √a²- [₁ 2(x+y) x² + y² giving your answer in terms of a. 1+ dx dy,

A: The given integral is  ∫0a2-x2∫-aa 1+2(x+y)x2+y2dx dy

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A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 2700 360 * 31, cos 0 = 1/8, 311/2 <0 < 2 ४ 1% کے too (1) ³+ (8) ²

A: given  cos∅=183π2&lt;∅&lt;2π there for ∅ is in 4 quadrant in 4 quadrant sin∅ is negative and tan∅ is…

Q: Let Give the 2,1 entry of 4-¹. a) 0-¹ b) 0¹/2 c) 03/2 d) 0-5 e) 0-2 f) O None of the above. 02 2 A-1…

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Q: Assume x and y are functions of t. Evaluate dy/dt for 2xy−2x+4y3=−56​, with the conditions dx/dt=…

A: Given: 2xy−2x+4y3=−56​, dx/dt=-16, x=4 and y=-2

Q: 6. Find the polar coordinates if (x, y) = (-√3, 1), r≥ 0, -2π <0 ≤0 (a) (2,117) (2,117) (b) (d)…

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Q: Determine whether the integral is convergent or divergent. 100 (x - 6)³ 8 S² O convergent O…

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Q: For the function y = x² + 2x find the value of dx when x = 3 and dy is 0.8. O - 0.2

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Q: Problem 3. evaluating them. ∞ 1 So₁² (2-3)³/2 5 dx Determine whether each integral is convergent or…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: ʼn object is thrown vertically upward whose height is given by the function s(t) = − 16t² + 35 here t…

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Q: Find y' if x = y*. C Note: Leave your answer in terms of ï and y. y

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Q: (5) Determine if the alternating series converges Σ(-1)^n. 8 n=2

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Q: Find the average temperature in the box D = {(x,y,z): 0≤x≤ In 4, 0≤ y ≤ In 8, 0≤z≤ In 16) with a…

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Q: 2. 2 S² X (x + 1)² dx

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Worldwide annual sales of smartphones in over a 5 year period were projected to be approximately q =…

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Q: dz Given z = xy + sin(xy2), with x(t) = 2t + 1 and y(t) = -t², find dt t=1

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Q: Evaluate the integral below taking as the region bounded by y = x and y = x². ]] (3x (3x + 1)dxdy

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Q: Problem 10. (a) an = n³ n³+1 Determine whether the sequence converges or diverges. (ln(n))² (c) cn =…

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Q: Why does it make sense to model the monthly temperature with a sine or cosine function? Part 2.…

A: We need to model trigo. function.

Q: Evaluate the definite integrals (show your solutions) sẽ có cos³ 3xsin3xdx

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Q: 3₂ If t=15157, evalvate if possible Part 1. Sin t 13 له b) none - 이글 e) 9 + ا (a C) - 0) ) 6)-1 یہ -…

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Q: The world population is approximately 6.1 billion, and can be modeled by the function P(t) =…

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Q: 17 Let I = [x² dx = 1596 and consider the Trapezoid Rule, T(n), and the Midpoint Rul 5 a. Compute…

A: Let's find T(12) and M(12).

Q: Find the intervals on which​ f(x) is​ increasing, the intervals on which​ f(x) is​ decreasing, and…

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Q: Approximate the area under the curve graphed below from x = 2 to x = 5 using a Right Endpoint…

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Q: Suppose a product's revenue function is given by R(q) 3q² + 200g. Find an expression for the…

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Q: 6. Use differentials to approximate the volume of a spherical shell whose inner radius is 5 cm and…

A: Note: According to our expert guidelines only one individual question is to be answered kindly…

Q: answer incorrect

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Q: Evaluate the integral 9 3 12 SS S 00 4y 9 3 12 SSS 0 0 4y (Type an exact answer.) 3 cos (x²) 4√2 3…

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Q: b) Ln=1 Inn n2

A: Given query is to find series converges or diverges.

Q: (b) Let rzi+yj + zk, and let r= ||r||. If f is a differentiable function of one variable, show that…

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Q: The linear approximation at where A is: and where B is: = 0 to sin (3x) is A + Bx

A: We need to find Linear approximation.

Q: For what values of the numbers a and b does the function f(x) axebr² have the maximum value f(1) =…

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Q: 2. (a) Draw the graph of f(x) = = 2x x 0 (b) Find lim f(x) and lim f(x) or explain why they do not…

A: follow next step

Q: Crystal is running a picture-framing business. Refer to the given break-even chart for her business…

A: The Solution is given below:

Q: Find the first five terms of the sequence of partial sums. (Round your answers to four decimal…

A: The given series, 12·3+23·4+34·5+45·6+56·7+.... We have to find the first five terms of the sequence…

Q: Find sin 2x, cos 2x, and tan 2x if sinx = - sin 2x cos2x tan 2x = 11 0 0 2 √13 and X terminates in…

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Q: a. Find a curve with a positive derivative through the point (1,1) whose length integral is given…

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Q: Expand the expression using the Binomial Theorem: x5+ 405 x+ 270 (3x - 1)5 = 243 15 x+ 1 x³+90 x² +

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Q: 6.) f(x) = HOLE(S) x²+x-2 (x+2)(x²-2x-15) VERTICAL ASYMPTOTE(S) HORIZONTAL ASYMPTOTE -10 10T 8- 8-…

A: The function is  f(x)=x2+x-2x+2x2-2x-15

Q: 21-22 Find y' and y". 21. y = x² ln(2x)

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Q: Consider the following. e¹ - 4x = 3 (a) Find the exact solution of the exponential equation in terms…

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Q: Write an expression for the nth term of the sequence. (Your formula should work for n = 1, 9,8 +12,8…

A: Given sequence:- 9,8+12,8+13,8+14,8+15,......

Q: 37-40 Find y' and y". 37. y = cos(x²)

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