1. Find the value of the directional derivative at the particular point Po for the given function in the direction of U. (a) g(r,y) = y² tan² r; Ū = -÷V3 i+; Po(}n, 2)

Q: A series is defined by Sn = £?=1 5* (a) Find the first 3 terms of the series (b) Use the method of…

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Q: EN tind an equation tor the line tangent to the Lurve at the point defined by the given t, Also find…

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Q: 2. [Growth of a tumor] When the radius of a spherical tumor is 6 mm, it is growing at a rate of 0.1…

A: To determine how fast the volume is changing.

Q: Find the missing values assuming continuously compounded interest. (Round your answers to two…

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

Q: 12sin3xcos7x dx

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Q: (a) Consider A B + X-1 7x2 - 17x + 38 C (x + 6)(x – 1)²- x+6 (x – 1)² (i) Use partial fractions to…

A: (7x2-17x+38)/[(x+6)(x-1) 2]=A/(x+6) +B/(x-1) +C/(x-1) 2

Q: sin' xcos³x dx 3

A: Given: I=∫sin7xcos3xdx   As we know that; The trigonometric identity; sin2x+cos2x=1 The Power rule:…

Q: (ii) Hence, evaluate 37x² – 17x + 38 J, (x + 6)(x – 1)²"

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Q: 2 (1 – :-) d.x

A: Solve the following

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 8x and…

A: There is a line through the origin that divides the region bounded by the parabola y=2x-8x2 and the…

Q: Evaluate the integral 5х — 2 dx (x + 3)2

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Q: Suppose an object moves along a line at 19 m/s for 0sts2 s and at 25 m/s for 2<ts5 s. Sketch the…

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Q: - numerical values only, do not type the units, space or comma.

A: here i am providing my handwritten solutio

Q: For the function S-22 + 3x if z <1 f(x) = | 2x + 2 if z 21' evaluate the limit lim f(x). (If a limit…

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Q: (a) Evaluate the double integral.

A: answer is in next step

Q: Evaluate the integral (Trigonometric Substitution) 4 x*dx (x² + 1)²

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Q: x² – 2x – 1 dx (x – 1)2(x² + 1)

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Q: | 3t³ (t² + 4)5dt

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Q: (2x + 6)dx x2 – 2x + 17

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Q: Ln(Sinx)dx

A: We need to solve D.E. NOTE - As per Bartleby's guidelines we can solve one question from multiple…

Q: f(1) . f'lx) dx

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Q: Find the equation of the tangent line to the curve y = 4sec z – 8 cos z at the point 4). The…

A: We can sole this as follows:

Q: 6y² -dA where D is the region in the 1st quadrant bounded by y =x' and y= 4x . Evaluate 9.

A: Here we have to evaluate the  integral of a function over a region.

Q: Evaluate the definite integral. i+e"j+t – (e~1 – 1) j + 5 i-ej+: (e – 1) i – (=" – 1) j + -1)j+극k i+…

A: We have to find the solution of  integral

Q: The functiof(x) and it’s first and second derivative are given: A) Domain of f(x) B)y intercept is…

A: Solution: f(x)=x-2x3 a) Domain :  take the denominator and compare it to zero x3 =0 =&gt; x=0

Q: Evaluate the definite integral. 1 |(7x2 - 4x +6) dx

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Q: whether the selic) H6 use un appropriate test to determine whether the" selics gilon wnverges or be…

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Q: the bot test to determine it the use tollowing series converges or diverges

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Q: tan x If f(x) = 3 sec a f (2) = f (1) =

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Q: An equation of the tangent line to a curve at the point (2, 4) is y = x + 2. if at any point (x, y)…

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t) ||r(t)||* r(t) = 8 cos(7t)i + 8 sin(7t)j + 3t

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Q: 1.) Determine the largest interval over which the function flx) = \x+3 is continuous. 2x 2.)…

A: 1) To find the largest interval on which the function f(x)=x+3 is conitnous.

Q: Find the exact length of the curve. 1 y = 1 < x < 2 4x

A: The given curve,   y=x33+14x, 1≤x≤2

Q: 30. The number of floats in the last Panagbenga Festival is about 50. This year, it is expected that…

A: Use permutations method nPr=n!/(n-r)!

Q: Using a trigonometric substitution, the integral dz becomes: 2+25 (a) 25 (tan 0) (sec 0) de (b) 5 /…

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Q: 14 of 19 Which of the following is a parameterization of the line that passes through the point (1,…

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Q: The point (4, k) lies on the ellipse 32 y? = 1. 18 Which of the following could be a value for k? 0…

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Q: For the function f(x) given below, evaluate lim f(r) and lim f(x). -2+3e 6e + 4 f(z) If the function…

A: We have to find out the limit

Q: 5. (r' -12r +43r? - 41r +5)÷(r –5)

A: Given query is to perform long division.

Q: 18 of 19 50 where T<0< 4r as shown in the diagram A rubber ball is being spun in a outward spiral in…

A: Let's find.

Q: 10. Consider the function defined by f(x) = Vr. Is ƒ differentiable at r = 1? at r = 0? at %D x =…

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Q: 4 x*dx J (x² + 1)²

A: Solution is given below:

Q: FIND THE GIVEN DIFFERENTIAL EQUATION Homogeneous Equation (x + y - 3) dx + C x -y + 1) dy • 0

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Q: An equation of the tangent line to a curve at the point (2, 4) is y = x + 2. if at any point (x, y)…

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

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Q: 2. Write the given (total) area as an integral. (vde a. The area above the x- axis and below y = 4–…

A: Here we have to find the area.

Q: х2 — Зх — 7 dx (x2 + х + 2)(2х— 1)

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Q: Determine which pair of points can represent as the absolute extrema of the given function at the…

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Q: xªdx J (x2 + 9)2

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Q: Evaluate the integral (Partial Fraction Decomposition) x +1 dx J (x² + 2)(x² + 1)²

A: First of all let…