lim -3x7 + 7x³ – 5. X→∞

Q: ㅍ (2) Evaluate (cos(3x) — sin(x))dx. - 6

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Q: x B 8- X x2-x-2

A: Given, x-8x2-x-2

Q: Find the angle between the vectors (6, 30√3) and (30√√3, 12). (Express numbers in exact form. Use…

A: let a→=6,303 and  b→=303,12

Q: Solve 3xy + y + x²y¹ = 0 (x² + cx) y³ = −1 (y² + cy) x³ -1 a. b. - c. (y² + cy) x³ = 1 d. (x² + cx)…

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Q: 1. Basic Integration a. fx(x + 1)dx b. S √ √x+x² dx x C. √₁²|x-1|dx

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Q: lim ln x x-0

A: Given:      limx→0 ln x Left hand limit:    limx→0-ln x As can be seen, left neighborhood of the…

Q: Let F(x) = f(f(x)) and G(x) = (F(x))²2. You also know that ƒ(7) = 2,ƒ(2) = 3,ƒ' (2) = 10, ƒ' (7) =…

A: The functions are Fx = ffxGx = Fx2 The values of the function fx and its derivative f'x are f7 = 2,…

Q: Given the function f(x) = 5x - 4, find the inverse function f-¹(x) =

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Q: For each of the four types of functions listed below, decide which of the pictures given represents…

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Q: e. lim n→∞ n k=1 4k ( n² - ) ) = n

A: Given : limn→∞∑k=1n4kn2−8n

Q: Question 12 Find the derivative of the function. (A) 15s¹4+70sº +30s¹ B 15s14-70s +30s¹ E 158¹4-70s…

A: Topic- Derivative of a function We are given, H(s)=(s10+6)(s5-7)and we know thatddssn=nsn-1

Q: 5. Consider the polar curves having the equations r = 3 sin 0 and r = 1 + sin 0. a. Sketch the…

A: Given curves are r= 3 sin(theta),r=1+sin(theta)

Q: 4. Use implicit differentiation on these. a) Find an expression for dy/dx at any point on the curve…

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Q: h(x)= (1x - 21 14 - 2x if x # 2 if x = 2

A: Given: At x=2, h(2) = 0. So, the function can be written as h(x)=|x-2|. And the function is…

Q: Find the equation of the tangent line. cuberoot(7x-6) that is perpendicular to the line 12x+7y+2=0

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Q: - · r(t) = (3t — t³, 3t², 3t+t³)

A: From the provided curve, rt, to determine the arc length from t=0 to t=b.rt=3t-t3, 3t2, 3t+t3

Q: If f(x) = (sin(x) S 4 + t dt and g(y) = = [ f(x). f(x) dx, find g^(1). 6

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Q: Find using partial derivatives. dx dy dx = x2/3 + y²/3 = a2/3

A: Given query is to find derivative of the expression.

Q: 1. Find the general solution to the DE dx - (4+e²x)dy = 0 2x ye ²x dx using two (2) methods with…

A: Given data÷ ye2xdx-4+e2xdy=0   1) First we use variable seperation method In that method seperate x…

Q: M S√2x = 1dx

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Q: 2 2. Is f(x) = { = { x²-1 x+1 if x = -1 if x −1 continuous at x = −1? (Show your work using limits.)

A: See this solution in below.

Q: The graphs of f and g are given. Use them to evaluate each limit, if it exists. If the limit does…

A: As per our guidelines we are suppose to solve only three sub-parts of a question. Kindly re-post the…

Q: A ball is thrown in the air. The path of the ball is represented by the equation h(?) = −t^2 + 8t.…

A: Given: h(t)=−t2 + 8t. For (a),

Q: ven (10, 5) and (x, - - 10), find all x such that the distance between these two points is 17. Sepa…

A: Topic:- calculus

Q: Find g'(3) given that f(3) = -2 and f'(3) = 4. a. g(x) = 3x² – 5ƒ(x) 2x + 1 b. g(x) f(x) . . e

A: Solution is done in steps

Q: Use Euler's method with step size 0.5 to compute the approximate y-values y1, 32, and y3 of the…

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Q: 9) For the function f, assume f(x)= continuous? A) 3/4 B) 1 4x C) 0 for nonzero X. D) 4/3

A: 9) The given function is ; f(x)=Sin(3x)/(4x).

Q: An airplane is flying at an elevation of 5150 ft, directly above a straight highway. Two motorists…

A: We need to find out the distance between the cars.

Q: 1. Find the derivative of each function using the FTC Part I arctant dt et b) dt (simplify your…

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Q: -4 -2

A: We have to find the following conditions according to the given information

Q: Comparing Simple and Compound Interest 100 10 Use the slider to see what happens over time.…

A: For simple interest, the interest is earned only on the initial Principal amount(P) while for…

Q: Find f'(x)) D f(x) (2) f(x) 3x³ +5x²12-2 2 6x -3x + 2x12 2

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Q: #4 #5 3 L (5+ JO (5+3 cos x) dx 3 [x²² O x² ex dx

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Q: the exact value of the trigonometric function at the given real number. (a) tan(-37) X (b) _csc(-37)…

A: See this solution in below.

Q: 5. The equation R(x) = -5x² + 15x + 20 models the revenue (profit-costs) of a company in hundreds of…

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Q: 3. An object is thrown vertically upwards with an initial velocity 20 ms ¹. The rate of displacement…

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Q: 1. During a rainy spring in the city of Fort Collins, Colorado, the following depth readings were…

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Q: valuate the integrals for f(x) shown in the figure below. The two parts of the graph are…

A: Given query is to find the value of the integral.

Q: oblem 8. (a) [e² sin (r) (b) [ (x+3) ln (x) (c) [²* (In (2))² da dx Calculate each of the following…

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Q: Determine whether the infinite series convergent find the sum. n=1 is convergent or divergent. If it…

A: The given infinite series is ∑n=1∞34n-45n We have to find its convergent and sum of the series

Q: Find the solution of the given DE. 7. +q=4 cos 2r; q(0)=1. dt

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Q: 5. The graph of f is given. Use it to graph the following functions. (a) y = f(2x) (c) y = f(-x) 1 0…

A: The given graph of function f

Q: Find the indefinite integral. (Use C for the constant of integration.) [ sin³ sin³ 30 √ cos 30 de

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Q: b. 14-x²|dx

A: I am attaching image so that you understand each and every step.

Q: compute the instantaneous slope at: (3,-4) Au

A: Let y=f(x)=13x2-4x+5

Q: r(t) = (t, ln(t), 0)

A: Given rt=t, lnt, 0

Q: Find the solution of the given DE. 10. +2²=2y√x

A: To find the solution of the given DE.dxdy+2xy=2yx

Q: Find Î(t), Ñ(t), Â(t), and the curvature x(t) for r(t) = (sin³ (t), cos³(t), 2), t€ (0,1). (Your…

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Q: d. e. Σ(**) - η 4k Τύπος (Σ(44)) - lim η-400 η k=1 - A C

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Q: In this problem you will calculate the area between f(x) = 5x + 9 and the x-axis over the interval…

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