1) Use a left-hand sum with 4 subintervals to approximate the following definite integral. Round to 4 decimal places. 5 [²³ x² + 4x dx S 3

Q: g(x) = x² - 2x x² - 4x +4 5 x² - 2x - 8 x2 − 5x+6 , x 2

A: g(x)=x2-2xx2-4x+4    , x<25                 ,x=2x2-2x-8x2-5x+6      ,x>2

Q: Find the indefinite integral. (Use C for the constant of integration.) sin³ sin³ 20 √ cos 20 de

A: To find the following indefinite integral.∫sin32θcos2θ dθ

Q: Solution of the differential equation dy y cos²x ytanx -cos^zsin²z 2 ₂ + c y² cos²x = sinºz+c z y³…

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Q: Find the following derivative and state a corresponding integration formula. 3x - 1 2x2 + 2x + 2 d…

A: Derivative

Q: 4. Use two different methods to solve the following problems. (If it's possible) a. fx(x² + 1)² dx…

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Q: 28. y² dx + (x² + 3xy + 4y²) dy = 0; when x = 2, y = 1. ANS 462v + y) ln v. 2 v

A: See this solution in below.

Q: 2) dy dx = 1 xy + y (separable equation)

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Q: Sketch the graph of an example of a function f that satisfies all the given conditions. lim-of(x) =…

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Q: Determine the interval(s) for which the function shown below is decreasing. Provide your answer…

A: Given query is to find the interval where function is decreasing.

Q: Find the most general antiderivative of the function. (Check your answ F(x) = 름 + 2x2 F(x) = 02-1

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Q: Find the equation of the tangent plane to the surface f(x, y) = x² + y² at point (3, 2, 13). 6x + 4y…

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Q: A 3.14 dT Consider the differential equation x +Tex with T(0) = 1. What is the approximate value dx…

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Q: Calculate the curvature of the cos(t²), sin(t²) >. Show all steps. parameterized curve r(t) =<

A: we need to calculate the curvature.

Q: ermine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

A: Given query is to find integral converging or diverging.

Q: dN N+² N = 1; N(2)=8.

A: A differential equation of the form dydt+p(t)y=q(t) is called linear differential equation and its…

Q: 4. Let In = f cos" xdx. Show that: In = 1 - Cos' n on-1 x sin x + n-¹ In-2, n ≥2. n

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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: 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: Please show your answer to 4 decimal places. Suppose that f(x, y) = e 2²-2y²-2x-y then the maximum…

A: See this solution in below.

Q: Problem 8. (b) √(x + 3) In (x) da 2 (c) for (in (In (x))² dx Calculate each of the following…

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Q: Consider the following function. 1 f(x) = x² - 3 Determine whether f(x) approaches ∞ or -∞ as x…

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Q: 2. The height of a golf ball after t seconds is given by s(t) = 24t - 4.9t² meters. (a) Find the…

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Q: Problem 4. Use the Substitution Rule to calculate each of the following integrals. You should show…

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Q: The left, right, trapezoidal, and midpoint rule approximations were used to estimate =1²₁ f(x) dx,…

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Q: The sales of a new high-tech item (in thousands) are given by the following function, where t…

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Q: lim x→16 1 √x-4 8 x-16

A: Topic- Limits We are given limx→161x-4-8x-16and we know thata2-b2=(a-b)(a+b)

Q: lim tan 7t t→0 t sec t ||

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Q: Find the equation of the plane which makes intercept 2,3 and 4 on the co-ordinate axes

A: Given data, a=2 b=3 c=4

Q: 24. (1 − xy)−² dx + [y² + x²(1 − xy)¯²] dy = 0; when x = = 1. 4, y = ANS. xy4y³ + 3xy - 3x − 3 = 0.…

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Q: Solve the Bernoulli differential equation 3(1+x²) y = 2xy (y³1)

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Q: Given: (0, 3.0), (2, 20.6), (4, 72.8), (6, 236.5), (8, 714.0), (10, 2209.7) Use the regression…

A: Given

Q: X lim x→0 √1 + 8x − 1 - ||

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Q: If f(x) = 3 x² 2 find f'(4).

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Q: 1. Sketch a graph of a function that has the features to match the following: i. It has x intercepts…

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Q: Enter an exact answer. Provide your answer below:

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Q: 7. Given to the right is the graph of a function f(x). Arrange the quantities below in order, from…

A: The graph of the function fx is To evaluate: The arrangement of f'(1), f'(2), f'(3) and f'(4) from…

Q: Problem 4. Use the Substitution Rule to calculate each of the following integrals. You should show…

A: As per our guidelines we can answer only 3 subparts of the given question so kindly repost the…

Q: Solve the Bernoulli differential equation 3(1+x²) y = 2xy (y³ - 1)

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

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

Q: 1. Evaluate 13/ 2x² + 3 (x² + 1)² by partial fractions. Hint: For the other integral involving (x² +…

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Q: Solution of the differential equation - ytanx = sinzcos² z y² is

A: dydx-ytanx=sinxcos2xy2

Q: 1. If an arrow is shot upward on the moon with a velocity of 58 m/s, its height in meters after t…

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Q: 3. Inverse trigonometric outcomes For this section, recall: du I Ja du -1 = sin-¹ ()+C, /du- -tan-¹…

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Q: [₂ (1-x-4x³. -2 •3 0 0 (1 − x − 4x³ + 2x5³) dx (5 + 3 cos x) dx 3 x² ex dx

A: Given that  some integration and we solve these integrations by using general property of…

Q: 0 -5 3) a) Given four points on the function y = f(x), A(-3,0), B(0,6), C(2,-2), and D(3,0), find…

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Q: Problem 8. (a) Je* sin (2) (b) ) [(x +3 (c) [²² +3) In (x) dx (In (x))² dx Calculate each of the…

A: As per the guidelines I am supposed to do the first question among multiple questions. So here I am…

Q: 2. Word Problem a. A ball is thrown downward with an initial velocity of -20 feet per second from an…

A: The position of a ball is found by equation of motion   S=So+ut+1/2(gt^2)

Q: by n equal width the width of each subinterval Ax in terms of the number of subintervals n. Ax=…

A: a. interval [ 0 , 2 ] number of interval = n

Q: You are given the four points in the plane A = (-7, -8), B = (-4, 7), C = (-2, -8) and D = (3, 3).…

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Q: 3. Use grad h(-3,4)=5ī +3j and h(-3,4)=10 to answer the following questions. a) Find the…

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