Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provided round brackets.. (a) Oppositely directed to v = (5, -14) and half the length of v. W (?, ?) (b) Length √5 and same direction as v = (8,0,−1). W = (?, ?, ?)

Q: Match the function with one of the graphs below using horizontal asymptotes as an aid. f(x) = 5+ H…

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Q: Question 6 The IBP formula fudv=uv - fvdu can also be written as fudv+fvdu = uv Which of the…

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Q: Y sinh(1) (use logarithmic differentiation) 3 (sec x)²/2[/cot-¹x]

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Q: Given the function f(n) = 3n¹ +33n³ +90n²: its f-intercept is its n-intercepts are

A: We can find the intercepts as below in the following steps.

Q: Determine the order of the given differential equation and state whether the equation is linear or…

A: Here we have to determine the order of the given differential equation and state whether the…

Q: /² sin sin ( π/4 x² dx (x²+4)5/2 (Use trigonometric substitution) fe2x+Inx² sin x² dx = = Find f…

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Q: = Find area of the region bounded by x² + y² = 4², 10y = -6x and 13y 8x where y > 0. Leave your…

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Q: How many different 8-digit phone numbers do not contain the digit 6? Assume that any digit in the…

A: To determine how many different 8‐digit phone numbers do not contain the digit 6. Assume that any…

Q: An object moving along a horizontal coordinate line has directed distance s(t) = 4t³ +9t² - 30t + 5…

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Q: 21. 5₁ 1 dx (A) 2 So to dx dx both diverge when p = xP (B) 1 © DO dx and (E) -1 HOR LAY A DUPA

A: Divergent

Q: IV. Find Do not simplify your answers. dy dx 1 1. cos x + y² = x coshy - 2y, where x > 0

A: Given problem:-

Q: . Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 4 4. lim loga (x+3)…

A: limx→1-log12(x+3)1-cosh(cos-1x)=limx→1- log2-1(x+3)1-cosh(cos-1x)since, limx→af(x). g(x)=limx→a f(x)…

Q: (measured counter- 1. A circle with radius 2 is centered at the origin (0,0). For an angle clockwise…

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Q: Find the directional derivative of f(x, y) = direction of Q(2,-2). NOTE: Enter the exact answer. √2…

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Q: Solve the given differential equation. All solutions should be found. dy 3x = e +9y dx NOTE: Use c…

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Q: 49-52 Sketch the curve and find the total area between the curve and the given interval on the…

A: We have to find the total area between the curve and the given interval on the x-axis.

Q: Let a = ci + j and b = 6i + 36j. Find c so that a and b are orthogonal. C = i

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Q: Find the partial derivatives of f(x, y) = x³y²

A: Solution ) f(x ,y ) = x3 y2 a) Partial differentiation with respect to x  fx( x ,y ) = 3x2y2 [ y is…

Q: Find the arc length of the graph of r(t) = ev NOTE: Enter the exact answer. L = 451 e√²ti + e-√² +…

A: Here we have to find the arc length of the graph of r(t)=e√2ti+e-√2tj+2tk , 0<=t<=√2ln5.

Q: The conic section whose equation is x2 - 3y2 - 8x + 12y + 16 = 0, is ______. centered on the origin…

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Q: Find the limit. lim (ti - 3j+t² k) 1-7 lim (ti-3j+t² k) 1→7 = i + i j+ k

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Q: 12. -s-7 (s+1)(S-2)

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Q: 2. Let f(x)=√(2-x)². Use the local linear approximation of f(x) at xo = 1 to estimate √0.99 (1.01)².

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Q: Describe the graph of the equation. r = (4 - 3t)i - 7tj O It is a plane in 2-space that goes through…

A: Given equationr=(4-3t)i-7tj

Q: 12 Give the properties for the equation 9x 2 + 16y 2 - 36x + 96y + 36 = 0 Domain -6 ≤ x ≤ 7 -7 ≤ x…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 2. lim (√²-x- (x² + x)

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

Q: (D4 − 1)y = 0

A: D4-1y=0

Q: Find volume of the solid bounded by z = 0, f(x,y) = x² + y², x² + y² = 4², 10y = -6x and 13y = 8x…

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Q: 31. (a) 32. (a) 33. (a) 34. (a) ₁12x-11dx • S²₁₂ √2+ |x|dx 2+ |x| L₁ let |e* - 1|dx *) ₁²³-1-15|dx +…

A:

Q: For each of the following integrations, choose the method that can be used to find its solution.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example,…

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Q: V. Given: 2. Find f'(2), if it exists. f(x) = el32-61-2, [2x - 5], √x²-9, if x 3 14

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

Q: 7 What is the probability of getting two heads and one tail when a coin is flipped three times?…

A: solving

Q: 4. Evaluate lim (cos x) ¹/2². 2-0

A:

Q: Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 4 4. lim log(x+3)…

A: Given: limx→1-log12x+31-coshcos-1x

Q: 2. y = tan-¹(cosh x) (sin² x) (sech x) secx [use logarithmic differentiation]

A:

Q: 3. S 2 x²+a² x4 = _ (x² + a²) ³² 3a²x3 -dx = + c

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Q: b. 36. Evaluate f(4x³ - 9x5 + 4x² - 6) dx. a. 32x7-45x + 8x + C 32x7 180x³ 4x9 C. b. 3 +8x + C…

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Q: 5-10 Find the area under the curve y = f(x) over the stated interval. 5. f(x) = x³; [2, 3] 7. f(x) =…

A: Area

Q: Use the formula ‹(t) = = 198 t7 k(t) : (4+121 +¹8) ²³/ = ||r' (t) x r"(t)|| r(t) = t²i+t¹¹j X to…

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Q: Give the properties for the equation 3y 2 - 2y + x + 1 = 0. Latus Rectum

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Q: SKETCHPAD Write the formula to represent the nth term of the following sequence. 6, 17, 34, 57, 86,…

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Q: 19. -π/2 21. -π/4 23. [³5e* dx sin 0 de cos x dx sec² 0 do (2x secx tan x) dx 20. rπ/3 22. 24. [¹-dx

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Q: our answers.

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Q: 17. 2x√/x dx 18. de xVx S

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

A: This question can be solved using the concept of dot and cross product of two vectors and…

Q: Find polar equation for the Cartesian equation 13y = 8x. a. theta = 1.02 c. theta = 0.55 d. r = 0.55…

A: Substitute x=rcosθ and y=rsinθ in 13y=8x. 13rsinθ=8rcosθ  13sinθ  =  8cosθ

Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A: Let's find.

Q: Integrating Factor by Inspection: 5. (xy-2y²)dx - (x²-3xy)dy = 0

A: (xy-2y2)dx-(x2-3xy) dy=0x(y dx-x dy)-2y2 dx +3xy dy=0dividing by xy2;(ydx-x dy)y2-2x dx +3y…

Q: Evaluate 5 (²) 4. dy -2

A: ∫-2-1 (y-2)dy/y ∫-2-1 (y - 2/y)dy [ 2y3/2/3 - 4y]-2-1 -2i/3 - 4i +42i +42i -14i/3 +82i