Find div F and curl F if F(x, Y, z) = xz°i+ 2y°x²j+ 2z²yk. 6 div F= curl F =

Q: Find the angle between the vectors (8, 6) and (-9, 7). Carry your intermediate computations to at…

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Q: Find the global minimum of the function f(x)=2x^3+3x^2–12x+4 on the interval [-4,2].

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Q: the

A: We will find the derivative.

Q: Verify Green's Theorem by evaluating both integrals aN dA Lv? dx + x² dy = ду ax for the given path.…

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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: Calculate x sin(y)dxdy

A: On solving this we will get

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

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

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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: sin(x) 19. Evaluate -dxdy by changing the limits of integration appropriately.

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Q: Find the volume of the solid bounded by the cylinder x2 + y2 =16 and the planes y=z, x=0, z=0 in the…

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

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Q: [2.xyy' – y² +, Vy* +x* ; 4– %3D

A: ∫x2+a2 dx = xx2+a22+a22lnx+x2+a2+C

Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→ ∞ x²

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Q: Find curl (4z i + 5x j + 3y k). Exact number, no tolerance. curl (4z i + 5x j+ 3y k) = (i )i + ( )j…

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Q: Utilize the Lagrange multipliers method to maximize the function f(x, y) = 8x + 18y - 10x2 - 4y2…

A: The given function is  f(x, y) = 8x + 18y - 10x2 - 4y2…

Q: 20. Evaluate dædy by changing the limits of integration appropriately. e y/2

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Q: 2r-4x2-x-3 dx x- 2r 3 In Ix+ 1 +3 ln|x-3| + C +1-3 ln|x-31+ C Option 1 Option 2 2 In |x + 1| - 3…

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Q: Find the exact value of: 1 + cot (Write your answer in the simplest form, use fractions whenever…

A: Trigonometric values cot2π6=32=3 sec2π4=22=2

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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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0,0). NOTE:…

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Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y 0, y= 4+ x°…

A: Here we have to find the volume.

Q: ах 2xy 2.xy +3y x +2xy dy dx

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Q: Find the vector 2u +3w given the vectors u =-i-4j and w = -2i + 5j. Write your answer in the form a…

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Q: Find V· (V x F), if F(x, y, z) = 7e"*i+ 9xe"j – 8e"²k. V· (V × F) =

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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 the line integral F. dr, vhere F(z, y) = -yi-rj and C is the curve y = v4-a from (2,0) to…

A: We have to find the line integral

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: 1. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

A: The solution is given in the next steps.

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: d d Calculate r1(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Use the formula k(t) = |r(t) × r"(t)|| ||r(t)||° to find k(t). 13 r(t) = e"i+etj K(t)

A: Solving

Q: Solve the following differential equations of 1- yy' = 2y – x; r'y'y'+ xy' = 1 dy x + v

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Q: The graphs of the function f (r) = 7 - a and g(a) = 3 are given below. %3D

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Q: Find V. (V × F), if F(x, y, z) = 5e"*i+ 6xe®j– 2ek. V · (V × F)

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Q: A swimming pool is circular with a diameter of 40 feet. Depth is constant along east-west lines and…

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Q: A forest fire is found at midnight. It covers 1100 acres then. It is spreading at a rate of f(t) =…

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Q: Use series to approximate | V1+ x*dx correct to two decimal places.

A: Let's find.

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

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Q: dx 2.

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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: Investigate the convergence of the following series. H.' 2n+5n 2) ΣΗ-1 ILJ! 3n

A: Here, the given series is: ∑n=1∞2n+5n3n Let, an=2n+5n3n; n≥1

Q: H.W (5) Solve the following differential equations of (x'+y')dx+(2xy cos y)dy phee

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Q: Evaluate the integral. (Use C for the constant of integration.) 2 cos (a) da sin(a)

A: Given query is to find the value of the integral.

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…

Q: Find the e v

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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: 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: Find G'(x). In(9) G(x) = (4e- 7t + 1) dt G'(x) =

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

Q: x+x-6 lim X-2 x-2

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