00 (n + 18)! Σ 18!n!18" n=1

Q: 4. Find the directional derivative of f (x, y, z) = e* cos(yz) the point (1,-2.0) in the direction…

A: I have authority to answer only one question, so  I am posting answer for 1 st question

Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

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Q: Given x = 2 lnt and y = 1+t, find the equation of the tangent line when t = 2. %3D O y=-4x-8ln(2)-5…

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Q: B- Find the length of the curve given by the position vector r=, =r'i+(1+(1/3)x')j+(1-(1/3)')k for

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Q: dx Vx4 – 2x² + 1 3,

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Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

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

Q: Cross-product of vectors   ⟨2,−1,3⟩×2⟨4,2,1⟩=?

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Q: Let C(x)=x²+4x+1 dol 5

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Q: Consider f(x) = cos (x) ln(x +2). a. Find the local linear approximation of f(x) at æo (In 2 =…

A: linear approximation of function fx=cosxlnx+2, at point x0=0

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Q: x° 16x6 -24x3 +9 dx

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Q: 2л + 3 dx 4г2 — 4х + 5

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Q: Find the total differential dw. 4. w = e*" – sin(yz) -

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Q: explain

A: We will check whether fundamental theorem of calculus applies.

Q: Determine the Laplace transform of 2et cos (6t - T). CO 8-4 3/3 (금) s2-8s+52 s2-8s+52 ㅇ (-) -85+52…

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Q: 5. e(2x- y) = 2x - y

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Q: Let C(x)= x2+4x+1 dollars be the cost function, where the x represents the quantity. The estimate…

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Q: Consider f(x) = cos (x) ln(x +2). a. Find the local linear approximation of f(x) at xo = 0. (In 2 z…

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Q: C Find the firet order parhal derivohve of fx,y,2). e W y-10y²23+ 43x hCs, t) =° t*In ts) + 32 4,5…

A: We want to find first order partial derivative of the given functions.

Q: Find all the second order partial derivatives of the given function. ​f(x,y)=xy2 + yex^2+5

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Q: ley'z ds, Cis the line segment from (3, 1, 2) to (1, 2, 5)

A: Given ∫c y2z ds Where c is the line segment from (3,1,2) to (1,2,5) Parameterize the line  r(t) =…

Q: By considering different paths of approach, show that the function below has no limit as…

A: In this question we have to find the limit.

Q: Question 8 Use differentials to find the approximate value of y: (2x 1)* when x = 0.98. O 0.88 O…

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Q: y 10 X -5 5

A: Range is all the possible value of y that is output of  defined x

Q: 3) (0,1,0), (2,1,0), (3,4,7) Ans. Indepena

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Q: What are the two values of k closest to -7 for which , sin2 (x +7)- cos2(x +7) da has a value of 12…

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Q: Using Laplace transform to solve the IVP: y" – 9y = e *, y(0) = 0, /(0) = 0 %3D we find the solution…

A: The given IVP is y''-9y =e-3t,   y(0) =0, y'(0) =0 To solve the problem we must know the following…

Q: C Fnd the firet order parho derivohve of 4.5 f(x,4,2)= e* +y2 1.

A: We have to find the partial derivatives.   According to our guidelines we can solve only one…

Q: 13. Evaluate the function. Give the exact value. cos tan (V3) cos(arctan( v3% )= 0.5

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Q: If the 6th term of an arithmetic sequence is 63 and the 14th term is 135, write the formula for the…

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Q: af Find if f(x,y) = ysin xy

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Q: Find all values of x for which the series converges. (Enter your answer using interval notation.)…

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Q: Create a function where the domain is not a set of numbers and the range would be the set of whole…

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Q: 1. Find the total differential dw. 2. w = re2u +e-V

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Q: In the year 1985, a house was valued at $110,000. By the year 2005, the value had appreciated to…

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Q: Plot the point that has the given polar coordinates.  2,  3π 4

A: We have to show the given point on the graph.

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: A manufacturer has an order for 1000 units of fine paper that can be produced at two locations. Let…

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Q: e 4e2 -8e+5 dx

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Q: |x = 3 sin´ (3t ) +1 ;teR = 2 cos (3t)–1

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Q: x=t² +3t +5 Determine the arc – length of the curve: y = (2t- +2

A: solution:-given curve x=t2+3t+5y=232t+43/2+2dxdt=2t+3dydt=22t+4

Q: 5) Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0.…

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Q: a spherical balloon is filled with gas at a rate of 300 mm3/sec. Find the rate at which the surface…

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Q: Let B be the sphere x2 + y? + z? = 1. The volume of the portion of B contained in the first octant…

A: Here, the sphere is x2+y2+z2=1 to find the volume formula for the spherical coordinates of it in the…

Q: For what values of x is fAx) increasing if f '(x) = 3-х (2r – 9)(x +4) %3D

A: We have to find the value of X in the function in which function is increasing.

Q: Select the correct answer. What is the value obtained by using left endpoints with n= 4 subintervals…

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Q: Solve the following initial value problem. f′′(x)=36x^2+30x+8, f′(−2)=−42, f(−2)=−15

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Q: b. dx Vr - 2x2 + 1

A: To evaluate: I=∫x5x4-2x2+13dx=12∫x22(x2)2-2x2+132xdx Substitute x2=u⇒2xdx=du

Q: Find the slope of the tangent line to the r=2-3cos 0 in polar coordinate at 0 =

A: Given:-r=2-3cosθdrdθ=3sinθTo convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y)…

Q: Q1: To integratef 6x + 8 dx we substitute a)x = sec 0 + 3 b) x = tan 0 + 3 c)x sec 0-3 d) x 3sec 0…

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