Solve (x² 1 + 2y) dx + (1 - x²) dy = 0; when x = 2, y = 1 1) (x + 1 + 2 ln x 1|) b. (x + 1) y = (x − 1) (x − 1 + 2 ln|x − 1|) c. (x 1) y = (x + 1) (x +1+2ln|x − 1|) a. (x + 1) y = (x Your answer is correct. The correct answer is: -

Q: d) Explain what happens to p't) for t greater than the value you found in part c. Give one reason…

A: p'(t) for t greater than the value of 10 becomes stable and reaches to a threshold value

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Q: Which of the following is a possible equation for the following trigonometric function?

A: To find which of the given equation is possible equation for the trigonometric function.

Q: 10. Find the area bounded by the curve x = y² + 2y and the line x = 3.

A: Area Bounded by the Curves : If f(y) and g(y) are two continuous function on a,b and f(y)≥g(y), then…

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Q: 1 a 3 2 1 a 1 To find the blue shaded area above, we would calculate: b Where: f(x)dx = area 1 2 3 4…

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Q: For the function ƒ(x) = x² – 11, find the equation of the tangent line at å = −12.

A: Given function f(x)=x2-11 We have to find the equation of tangent line at x=-12 Derivative of a…

Q: 1. (a) Use the Euclidean Algorithm to find ged(125, 793). (b) Using the workings in (a), find m, n €…

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Q: 12. Determine whether the following is true: (a) ≥3, EZ, 31(2²" - 1); n (n + 1)(2n +1) (b) 12+22+ 32…

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Q: A y 10+ -10-8 -6-4 -2 8 9 2 2 7 6 8 -10- 2 45 8~9 10 X

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Q: 1. The graph of y = f(x) is given below. -4 2 2 a) Find lim f(x) or state why it does not exist. 7+1…

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Q: Solve x (az + √2) dx y (az + √2) sin (ay²) dy + (az − √2) dz = 0 4√/2ln |az + √2 = C 4√/2ln|az +…

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Q: Compute the rotated area bounded by y = 2x, x = 2 and x-axis about x-axis

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Q: Evaluate are f(4) And solve f(x)=1

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Q: Consider the curve r(t) = (5t² − 3)i + (3t - sin(t))j. - y -5 5 a(t) = -5 5 10 15 20 (a) Find the…

A: The given curve rt=5t2-3i+3t-sintj use the derivative formulas, ddttn=ntn-1ddtsin t=cos tddtcos…

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Q: Question 4 Use Laplace transforms to solve the differential equation: d²x di 2 + 4x = cos(21) where…

A: Topic:- application of integration and differential equations

Q: The function f is graphed below. State the values that fulfill the following requirements. If there…

A: Please see the below picture.

Q: Calculate S√4-x² dx

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Q: Consider the following function. f(x) = x² - 4x + 5 (a) Find the critical numbers of f. (Enter your…

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Q: Given r(t) = (set, et cos(t), et sin(t)), determine each of the following. (a) the unit tangent…

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Q: y(x tan x + In y) dx + tan x dy = 0.

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Q: 4. y = x cos(In x) x²y" - xy + 2y = 0

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Q: 2. If f: R→→ R satisfies f(1) = 3 and f'(x) ≥2 for all x's, how small can f(7) be?

A: Here we have to find the smallest value of f(7).

Q: −5x – 5, f(x) = 2x² + 2x - 1, x < -1 x ≥ −1

A:

Q: functions f (x) = 2 and g(x) = 1 (i) Consider the (a) Write down the domains of the functions f (x)…

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Q: A fast-food restaurant has a cost of production C(x) = 14x + 108 and a revenue function R(x) = 82.…

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Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…

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Q: What is the radius of convergence of the series R=2 b. R=1 R = ∞ d. R=0 a. C. +∞ xn n+1 -?

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Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

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Q: Find the the macl following:

A: Here, we need to find the Maclaurin series of tan-1x1+x2. Now,        Maclaurin series of function…

Q: Find the slope of the tangent line to the curve 2x² 4xy + 4y³ = 10 at the point ( − 1, 1).

A: SOLUTION-

Q: -6-5-4-3-2-1 у 7г 6 4 3 2 1- -1 -2 -3 -4 -5 -6F 1 2 3 4 5 6

A: Range :- all the y value where function is defined

Q: Compute the length of the curve r(t) = (-4t, 5t — 3, -2t + 3) over the interval 0 ≤ t ≤9 L =

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Q: h. Use the second derivative to identify intervals where f(x) is concave up. (-0,3) X i. Use the…

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Q: Let y = tan(2x + 2). Find the differential dy when z = 5 and dr = 0.2 Find the differential dy when…

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Q: A1. SOLVE STEP BY STEP IN DIGITAL FORMAT Using the following function and the given intervals…

A: Given - f(x) = 4x^2 - 6                [ 3 , 6 ] ∆y/∆t =[ f(X2) - f(X1) ] / ( x2 - X1)

Q: d the equation of the tangent line to the curve y = 5x cos x at the point (7, e equation of this…

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Q: f(x) = = -2x² + 7 7x - 10 if x -1

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Q: VIBDIC he following DES. to E visbiol

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Q: Sketch the region enclosed by y = 7x and y = 9x². Find the area of the region.

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Q: y-e-x4cos4x ស

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Q: 3. State the components of a unit vector that is perpendicular to the vector = (5,2,−1).

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Q: 4) Find the equation of the line tangent to h(x) = (2-x)(x³ +4x-4) at x=1.

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Q: Given f''(x) = 3x + 3 and f'(-3) Find f'(x)= and find f(2) 1 and f(-3) = 5.

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Q: egrate the following by hand, shc 9 (a) 3 3 √x³ - 24+8) dx

A: We can solve this as follows:

Q: What is the equation of the tangent line to y=−2x^3−x^2+4x+3 at x=3? Write the tangent line in…

A: We have to find the equation of tangent line.

Q: - п/2 эт/2 п/2 0 п/2 3г/2 5г/2

A:

Q: 4 sin(x - 2) x→2 3 ln (3x – 5) Evaluate lim and write your answer in simplest form.

A: We can find the limit in the following steps.