0.3 77. Prove that 0.0198 < sin x dx < 0.0296. Hint: Show that 0.198 < sin x < 0.296 for x in [0.2, 0.3].

Q: a. f(x) = x³ tan x + 9x-4 b. f(x) = cos x 5 18-secx iniog srt 16 S+x8-x=xvius srit of enil Inggrist…

A: (a)  f(x)=x3tanx+9x-4formula used (i) d dx(xn)=nxn-1(ii) d dx(tanx)=sec2x(iii)  d…

Q: Letr> 2. Show that sin² r - sin² 2 r-2 < 2. Justify your answer. Hint: Apply the Mean Value Theorem…

A: Let r&gt;2.   To Show: sin2 r-sin2 2r-2&lt;2.

Q: Find the equations of both of the tangent lines to the ellipse x² + 4y² = 36 that pass through the…

A:

Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: 16. Evaluate ft tan5 x sec¹ xdx.

A: We know that Sec²x = 1+ tan²x ∫ xn dx=( xn+1)/(n+1)

Q: Let f(x) = sin x. Using a calculator, we find 2 0.707, f (-- 0.1) 0.633, f fG +0.1) 0.774 Use these…

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Q: for a -1 2x +5 f (x) = If fis the function defined above, then f' (-1) is A -2 B 3. E) nonexistent…

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Q: 8. If tan x = 3, the numerical value of vcscx is (A) 0.32 (B) 0,97 (C) 1.03 (D) 1.78 (E) 3.16

A: Given: tanx=3 we know that cosec2x=1+cot2x

Q: S car'x dx cos

A: To find: The value of ∫cos4x·dx. Given: The integration is ∫cosnx·dx=sin x·cosn-1xn+n-1n∫cosn-2x·dx…

Q: 6. Determine the intervals on which the following function is increasing or decreasing f(x) = sin r…

A: Note here we need a interval to find out where function increasing and decreasing because it is a…

Q: 6. Approximate the real root of x – cosx = 0 to three decimal places. Let xo = 0.8 and find x1, x2,…

A: Let f(x) = x - cos(x) x0 = 0.8 By using the Newton-Raphson method to approximate the root,…

Q: 1. Differentiate. Do not simplify. а. f(0) = 3cos(0*)sin(0³ – 2) b. f(x) = 4x + 25-x² + 2x-1

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Q: 10V dx (1+x³/2)² 1 Evaluate Evaluate J. So Vē cos (03/2) de I

A: (1) Let t =…