44 If 2x=y¹/5 +y=1/5, then express y as an explicit d²y dy = 25 y. dx dx² function of x and prove that (x² - 1) + X.

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Q: 17. f(t) is the graph shown below and g(x) = f f(t)dt. Find g(0), g(1) and g(4). D 2 3

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Q: 1. (6413 #4 p. 351) The cross section of a large tank is a trapezoid. The short side of the…

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Q: 12) y = 2-X; dy 3x+1 A) -7 (3x+1) dy = ? ² B) 6X-5 (3XH) 2 c) (3x+1) D) = ¹ 3+2X

A: NOTE: Refresh your page if you can't see any equations. . take derivagive

Q: If h(2) = 5 and h'(2) = -2, find d (h(x) dx X x = 2

A: given  h(2)=5  and  h'(2)=-2find   d dx(h(x)x)  at x=2we know   d dx(ab)=bdadx-adbdxb2

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Q: Differentiate the function. V'(t) = V(t) = t-3/5 + +t²

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Q: Find the particular solution of the D.E. y "+ 3y + 2y = 4e° = 4e* ON =e* 2 Oy₁ = / = Ae* + B

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Q: Differentiate the function. 4√x + 9x 7x² y' = y =

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Q: •24-x2 신 0 0 -4-y 0 x dzdydx

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Q: Find the equation of the line through the y-intercept of y = x²¹ - 9x5 −7+ 9x² and the x-intercept…

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Q: 15

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Q: Q lan for the conic based Yon: Ellipse with major verti #) and a focus point at (9,4_ = sketch and…

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Q: 5 5. Given that sin x== 13 (a) cos(x-y); 2√5 5 x is in Quadrant I, and cos y =—- y is in the…

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Q: 4. Trace the curve: y² = x²−4x−12 x²-2x-3

A: for x intercept put y=0for y intercept put x=0y2=x2-4x-12x2-2x-3

Q: U. Solve the given equation 1) sec x(2 sin x-√2)=0 T Answer: x==+2nk, 4 TT ak 3π x== +2 4

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Q: Differentiate. g'(0) = g(0) = eº (tan(0) — 0)

A: dexdx=ex  d(tanx)dx=sec2xd dx(a.b)=adbdx+bdadxgiven  g(θ)=eθ(tanθ-θ)

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Q: 10) Does the sequence an = √n² + 3n - n converge or diverge? Explain

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Q: (D7 + 2D6 + 7D5 + 14D4 + 8D³ + 16D² - 16D - 32) y = 0

A: The given differential equation D2+2D6+7D5+14D4+8D3+16D2-16D-32y=0. We have to find the general…

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Q: 9- The sum of the first 10 terms of an arithmetic sequence is 235 and the sum of the second 10 terms…

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Q: 9. Use the comparison theorem to show that So L'√T- 10. Find √1 + x² dx ≤ Also show that ²√1 + x dx…

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Q: Consider each function to be in the form y = kx, and identify k or p as requested. Answer with the…

A: Given function y = k.xpy = 1πx

Q: (c) sin 13л 15 COS Зл 15 COS 13п 15 sin 3п 15 Answer: sin 10п 15 = sin (2) 3 2п √√3 =

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Q: Determine the solution of the following differential equations. c) (D¹ + 2D6 + 7D5 + 14D4 + 8D³ +…

A: To determine the solution of the following differential equation.D7+2D6+7D5+14D4+8D3+16D3-16D-32y=0…

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Q: 14. Given g(x) = f(t². + 6t16) dt, find intervals on increasing / decreasing and concave up/ concave…

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Q: 14. The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30…

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Q: The graph of f is shown below. Evaluate each integral by interpreting it in terms of areas f f(x) dx…

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Q: Consider the following functions. f(x) = x², g(x)=√x-7 Find (fog)(x).

A: Given,            fx=x2 , gx=x-7

Q: ← dy (a) Show that y* +x-6=0 is an implicit solution to dx Part 5 of 6 1 on the interval (-∞,6). 4y…

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Q: Work of 1 Joules is done in stretching a spring from its natural length to 11 cm beyond its natural…

A: Given: Work done, W = 1 Joule Strech of the spring, x=11 cm = 0.11m   Now, The spring constant is…