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16. Solve the following equations for solutions on (b) 2cos 3x = 1 (a)sec² x 2x2tan²x=0 [0, 2π): (c) sec 2x=4tan² x (d) tanæ sin x-tan x=0

16. Solve the following equations for solutions on (b) 2cos 3x = 1 (a)sec² x 2x2tan²x=0 [0, 2π): (c) sec 2x=4tan² x (d) tanæ sin x-tan x=0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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10. Evaluate the following limits assuming that_lim_f(x)=3 and_lim_g(x)=1: (c) lim 9(*) #114 72 (a) lim f(x) g(x) H-4 (b) lim 2f(x) + 3g(x) x→-4 12. Suppose that lim g(h) = L. 11. Assuming that lim = 1, which of the following statements is necessarily true? Why? f(x) x0 x (a) f(0) = 0 a) Explain why lim g(ah) = L for any constant a ‡0. h→0 13. Use the Squeeze Theorem to prove that if lim|f(x)|=0, then lim f(x)=0. I→C = {₁ (b) lim f(x)=0 x b) If we assume instead that lim g(h) = L, is it still necessarily true that lim g(ah) = L? h-1 c) Illustrate (a) and (b) with the function f(x)=x² +1. (a) f(0) = X→C T²-c if x < 5 4x + 2c if x 5 14. Find the value of the constants (a, b, or c) that makes the following functions continuous: if x < -1 (b) f(x) = ax+b if-1<x</ x-1 if x > 1/1/ f(x) +1 439(x) 9 (d) lim x 16. Solve the following equations for solutions on [0, 2π): (a)sec² x - 2tan² x=0 (b) 2cos 3x = 1 15. Use the Intermediate Value Theorem to find an interval of length containing a root of f(x) = x³ + 2x +1. (c) sec 2x=4tan² x (d) tan x sin x-tanx = 0
Transcribed Image Text:10. Evaluate the following limits assuming that_lim_f(x)=3 and_lim_g(x)=1: (c) lim 9(*) #114 72 (a) lim f(x) g(x) H-4 (b) lim 2f(x) + 3g(x) x→-4 12. Suppose that lim g(h) = L. 11. Assuming that lim = 1, which of the following statements is necessarily true? Why? f(x) x0 x (a) f(0) = 0 a) Explain why lim g(ah) = L for any constant a ‡0. h→0 13. Use the Squeeze Theorem to prove that if lim|f(x)|=0, then lim f(x)=0. I→C = {₁ (b) lim f(x)=0 x b) If we assume instead that lim g(h) = L, is it still necessarily true that lim g(ah) = L? h-1 c) Illustrate (a) and (b) with the function f(x)=x² +1. (a) f(0) = X→C T²-c if x < 5 4x + 2c if x 5 14. Find the value of the constants (a, b, or c) that makes the following functions continuous: if x < -1 (b) f(x) = ax+b if-1<x</ x-1 if x > 1/1/ f(x) +1 439(x) 9 (d) lim x 16. Solve the following equations for solutions on [0, 2π): (a)sec² x - 2tan² x=0 (b) 2cos 3x = 1 15. Use the Intermediate Value Theorem to find an interval of length containing a root of f(x) = x³ + 2x +1. (c) sec 2x=4tan² x (d) tan x sin x-tanx = 0
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