Find V. (F x G), if F(x, y, z) = 3.xi +j+ 6yk and G(x, y, z) = xi + yj – zk. V· (F x G)

Q: Describe the graph of the equation. r = (5 – 21) i + 7tj O Itis a line in 2-space through the point…

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Q: 4.Graph one cycle of function given below. State domain, range, period, phase shift, vertical shift…

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Q: Matching Type. Match the functions in Column A with their corresponding derivatives in Column B.…

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Q: 25. The graph of y = a* +b is shown below. Find the EXACT values of a and b. 6- (2,5) 4- 2- y = a*…

A: This question is based on substitution of points.

Q: The water level in a glass decreases 0.4 cm each hour due to evaporation.  At the beginning of the…

A: The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the…

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Q: Let F(t) = Find a parametric equation of the line tangent to F(t) at the point (111, 648, - 4.394)…

A: Let r→t=4t3+3, t5+5t4, -2 ln3tTo find the parametric equation of the line tangent to r→t at the…

Q: 13. Solve the following system of equations using either the substitution method or the graphing…

A: Linear equation: Linear equations are first-order equations. An equation with a homogeneous variable…

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A: Given,             limx→1x2-4x+3x2-x

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Q: integrate (2x + sqrt(x)) dx from 3 to - 6 A. 27 +2√3+4√6 B. 27 + 2√3 C. 27 - 2√3+ 4√6 D. 27-4√6

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Q: Solve

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Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: fast is the area of the rectangle changing at the instant when the other side is 12 cm and…

A: Topic:-  application of derivatives and geometry

Q: d Calculate ri(t) r2(t)] and rı(t) x r2(t)] first by differentiating dt the product directly and…

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Q: Find the arc length L of the graph of r(t). r(t) = 5 cos(t)i + 5 sin(t)j + tk, 0<t< 2n L =

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Q: Find the first partial derivatives with respect to x,y and z. f(x. y.z) - 3x°y - 9 xyz + 10 yz %3D

A: Find first partial derivative

Q: 5x + 2lnx 8. lim X+3Inx

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Q: How?! e den -e-x ex 2.

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Q: Let F(t) = * F(e)dt (dont include the «C) Fine Question Help: D Video Add Work

A: We know, ∫tndt=tn+1n+1 ∫-sin-tdt=∫ddt-cos-t=-cos(-t)

Q: 2. The volume of the sun is 1.4 x 10 cubic kilometers and the volume of the earth is 1.1 x 102 cubic…

A: Earth mass

Q: From 1990 to 2000 the student tuition at a University grew from $12,000 to $18,000. (a) Using the…

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Q: Find the norm (or length) of v = <-2, 3)

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Q: x* +x² 5. lim,-. e* +1

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Q: (4x-3) find dy/dх y = (2х-7)6

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Q: d dri(t) • r2(t)] = d [ri(t) × r2(t)] dt ||

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Q: 3. Find the area of the region inside the circler-3 sine and outside the limacon r= 2 - sine. Sketch…

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Q: please

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Q: Solve the following integrals: 1. S–7e*dx 4. S 8*+1dx -6 2. S(2e* – 6*)dx 5. S-dx 3. S;(3")dx 6.…

A: ∫ex dx = ex+C ∫ax dx = axln a+C ; where, 'C' is an integration constant. Note : As per our…

Q: Consider the following functions. f(x) g(x) = 8 sin x = 8 cos 2x | 2 6

A: The objective of the question is evaluate the area of the given bounded region.

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 sts 1. (y – x) dx +…

A: A detailed solution is given below

Q: Find the area of the region bounded by the given equations. Clearly state the integral(s) used to…

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Q: Find T(t) and N(t) at the given point. r(t) = 9 cos(t)i +9 sin(t)j + tk; t = 2 || T(;) N ||

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Q: Evaluate the iterated integral. 1/4 y cos(x) dy dx

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Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. x + 3y2) dy

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Q: Determine whether the improper integral diverges or converges. -6x dx O converges O diverges…

A: This is a problem related to indefinite integral. Based on the general formula and concept we will…

Q: 1 Find the length of the curve y (x2 + 2)3/2 from x = 0 to x =9. 3

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Q: 5. Which of the following is equivalent to (v2/2 – iv2/2) ? O -2 O 1 O -1/2 O -1 O 2 O 1/2

A: We have to find the equivalent of given complex number.

Q: 5) FIND THE MACLAURIN MALLAL fOR SERIES fa)=x cos (2x) %3D

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Q: Using an appropriate substitution, cos x-sin x the integral 3. dx equals: 0 cosx+sin x O none of…

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Q: lim (t i - 6 j +1° k). -5 (t i – 6 j + r² k) = i i+

A: Topic:- limit and calculus

Q: 2x² +2y? 11. Set up an integral that would calculate the volume of the solid bounded by the…

A: Given problem:- 11. Set up an integral that would calculate the volume of the solid bounded by the…

Q: Find f(x) given that f'(x) = V+ x² and f(0) = 2.

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Q: of tue reigon boundrd by the graph of tue algebraic fundin. 2) Find tue asea f(x) = x+12x +36 2 =…

A: Given

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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

Q: 7) FIND EQUATION Of THE TANGENT AN LINE TO THE PARAMZTRIL X=t-+もt こe AT t =0. CURVE

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Q: ) Find an equation of the line tangent to the curve y = x²e²-3 at a = 3.

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Q: 2x 1- cos x Graph f(x) = sin for Osxs2x by using transformations. 2 2- Use the graphing tool to…

A: To find: the graph of sin2x2 = 1-cosx2 for 0≤x≤2π Graph of cosx will be as following

Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (9t + 4)i + tj, 0 sts 1

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