4 Find sin 2x, cos 2x, and tan 2x if sin x = and x terminates in quadrant II. 5 sin 2x = S ? cos 2x = tan 2x = X

Q: Question Evaluate the indefinite integral given below. [ (sin³ (sin³ (x) - 3 sin² (x)) (sin (x) — 4…

A: Given,             ∫sin3x-3sin2xsin4x-4sin3x6cosxdx

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A: This is a problem related to integration of the function. Derivative is given now by performing…

Q: 13. What is 2sinx cos x dx? TRONG A. +C In 2 C. 2 cos.x B. +C 2sinx In 2 D. In 2 14. Which of the…

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Q: 2. Write the given (total) area as an integral. (3 points each) a. The area above the x-axis and…

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Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x - y³ dy=0 is

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Q: Jo (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (3,-5) X Evaluate -30

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A: We have to solve  ∫dx1 + x-23.

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A: Here we have to find the indefinite integral.

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A: Use simple differentiation formula.

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Q: Evaluate the iterated integral. 7 2 z z [ [²] ² 1 -1 J-y Y (-72+3 ln (7)) x dx dz dy

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Q: dy dx +y=e*

A: The standard form of the linear differential equation is; dydx+Py=Q Where, P & Q is the function…

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Q: = cot = C C In (x² + y²) + 4 arccot =

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Q: Scos2x (2 cos2x-1) dx

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Q: Verify Green's Theorem by evaluating both integrals AN fx2ax+x²&y-LI (x-an) = y2 dx + x2 dy dA ?х ду…

A: We can solve as follows

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A: d3ydx3-d2ydx2-dydx+y=0                (1)LetD=ddxTherefore   equation (1)…

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Q: Use Green's Theorem to evaluate the line integral a-x)dx + (2x - x) d for the given path. C:…

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Q: Find the absolute extrema of f on [-2, 3] if f(x) = x² - 6x - 1 O √5 O 2

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Q: x1/2 dx x3/4 + 1 Let x = z8 dx = 8z7dz Is the substitution the most appropriate one? Explain your…

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A: Given :

Q: 4. (y² cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e

A: exact differential equation

Q: 5. Consider the surface obtained by rotating the graph of f(x) = 1/2, 221, around the z-axis. This…

A: We will show this using integration ∫1∞1xdx = ln x1∞ = limx→∞ln x = ∞

Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

A: The Maclaurin series for f(x) is given by f(x) = f(0) + f'(0)1!x + f''(0)2!x2 + f'''(0)3!x3 + …

Q: √25x2-4 -dx, 2/5 cosø dø 2/5 sec^2 ødø 2/5 seco tanø dø None of the choices

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Q: = ||r' (t) x r"(t)|| ||r' (t)||³ to find k(t). r(t) = 11 cos(t)i + 11 sin(t)j + 6tk Use the formula…

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Q: Find the exact area under the graph of f(x)=1 between r=0 and r = 2. Area =

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Q: Solve the following Bernoulli’s differential equations 2ydx + x (x^2 ln y - 1)  dy = 0

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. So||ti + Bij||dat 1717- = 13 X

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Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

A: The given geometric series :35+925+27125+...The geometric series can be written as:an=3535n-1 where…

Q: 4. dx +

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A: Here we have to solve the given integration.

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Q: 343 2 1. y = x² - 9 and y = x + 3 (Answer: 6 s. u.)

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Q: Question 15 Find the derivative of y = 32x+5 A. 2 ln 3 (3²x+5) B. In 3 (3²x+5) C. 2ln 3 D. 32x+5 O B…

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Q: Find the limit. lim (ti – 4 · 4 j + t² k) t→7 lim (t i − 4 j + t² k) = i 1→7 i+ i j+ i k

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Q: For a non-negative function f(x), an approximating formula for the area under curve using a uniform…

A: The area approximation formula is Area≈∑fci∆xi=1n. Where fci=Height of the ith rectangle   ci…