154. We can obtain a useful linear approximation of the function f(x) - 1/(1 + tan x) at x- O by combining the approximations 1-x and tan I- x to get 1- x. 1+ tan x Show that this result is the standard linear approximation of 1/(1 + tan x) at x- 0.

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A: x 0 π4 3π4 π2 π 5π4 3π2 7π4     tanx 0 1 3 ∞ 0 -1 -∞ -3

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Q: What is special about the functions f(x) = sin x - 1 x + 1' x 2 0, and g(x) = 2 tan Vĩ? -1 Explain.

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A: Given

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Q: Consider the function f(x) = sin2 (x) − sin(x), 0 ≤ x ≤ 2π. Find any x-intercepts of f(x) on [0,…

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A: Just observe that its value of tan(30°).

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () <0, f(x) has a root in [0]. If we use…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ (x) has a root in [o,]. If we…

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Q: 52. Verify that f(x) sin x is an odd function and u fact to show that '3 sin x dx < 1 -2

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Q: 26. Show that the function has removable discontinuity at the origin sin 2x {²7, 2x 1 f(x) = if x =…

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Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

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