Question
Asked Oct 10, 2019
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Problem 2 please

Problem 1. Simplify
a) In(e5) In(e6) In(e7) =
b) 5l0gs 123
algebraic expression for sin(cos (3)) =
Your answers should not contain any trigonometric or inverse trigonometric function.
- 1
Problem 2. Find an
0 for
Problem 3. If possible, find values for a and c that make f continuous at r
1
sin (ax)
if x<0
2т
if 0
f(x) =
с
if 0 x
VI+4-2
Problem 4. Find the limit if it exists. If the limit does not exist, explain why it does not.
2+1
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Problem 1. Simplify a) In(e5) In(e6) In(e7) = b) 5l0gs 123 algebraic expression for sin(cos (3)) = Your answers should not contain any trigonometric or inverse trigonometric function. - 1 Problem 2. Find an 0 for Problem 3. If possible, find values for a and c that make f continuous at r 1 sin (ax) if x<0 2т if 0 f(x) = с if 0 x VI+4-2 Problem 4. Find the limit if it exists. If the limit does not exist, explain why it does not. 2+1

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Expert Answer

Step 1

To find:

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Step 2

Let us assume the following,

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1 3x 1 cos a (3x) COs a = adjacent side We know from the trigonometric ratio that cos a hypotenuse So, we draw a right-angled triangle with an angle of a cos3x with adjacent side as 3x and hypotenuse as 1 A 1 a В C Зх

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Step 3

Note:

...
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According to Pythagoras theorem, sum of square of two legs of triangle is equal to square of hypotenuse, Thus, AB2(3x)2 = 12 AB2 12 (3x) 12 - (3x)2 V1-9x2 AB = АВ Now, we find sin (cos1 3x) using the trigonometric ratio for sin a. АВ opposite side sin a = hypotenuse АC 1-9x2 sin (cos 3x) -1 1 = V1 -9x2

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