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(a)
To calculate:The exact value of function
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 118E
The value
Explanation of Solution
Given:
The functions
Formula Used:
Use the property
Use another property
Calculation:
Substitute the values of
Substitute
By the trigonometric identity
Substitute
And,
Therefore,
By the trigonometric property
Substitute
And,
Now substitute
Now substitute the values in the formula.
Therefore the value
(b)
To calculate:The exact value of function
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 118E
The value
Explanation of Solution
Given:
The functions
Formula Used:
Use the property
Use another property
Use another property
Calculation:
Substitute the values of
Substitute
By the trigonometric identity
Substitute the values in above equation.
By the trigonometric property
Substitute
And,
Now substitute
Now substitute the values in the formula.
Therefore the value
(c)
To calculate:The exact value of function
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 118E
The value
Explanation of Solution
Given:
The functions
Formula Used:
Use the value of
Use the property
Calculation:
Substitute the value
Substitute
By the trigonometric identity
Therefore,
By the trigonometric property
Substitute
Now substitute
Now substitute
Therefore the value
(d)
To calculate:The exact value of function
(d)
![Check Mark](/static/check-mark.png)
Answer to Problem 118E
The value
Explanation of Solution
Given:
The functions
Formula Used:
Use the property
Use another property
Use another property
Calculation:
Substitute the value
Substitute
By the trigonometric identity
Therefore,
By the trigonometric property
Substitute
And,
Now substitute
Now substitute the above values in the formula.
Therefore the value
(e)
To calculate:The exact value of function
(e)
![Check Mark](/static/check-mark.png)
Answer to Problem 118E
The value
Explanation of Solution
Given:
The functions
Formula Used:
Firstly calculate the angle
Use the identity
Calculation:
As
Substitute the value
By the trigonometric identity
Therefore,
By the trigonometric property
Substitute
By the trigonometric property
Substitute
Now substitute
Therefore,
Therefore value
(f)
To calculate:The exact value of function
(f)
![Check Mark](/static/check-mark.png)
Answer to Problem 118E
The value
Explanation of Solution
Given:
The functions
Formula Used:
Use the property
Use another property
Calculation:
As
Therefore,
By the trigonometric property
Substitute
Now substitute
Now substitute
Therefore the value of
Chapter 4 Solutions
Precalculus with Limits: A Graphing Approach
- Let f be a function whose graph consists of 5 line segments and a semicircle as shown in the figure below. Let g(x) = √ƒƒ(t) dt . 0 3 2 -2 2 4 5 6 7 8 9 10 11 12 13 14 15 1. g(0) = 2. g(2) = 3. g(4) = 4. g(6) = 5. g'(3) = 6. g'(13)=arrow_forwardThe expression 3 | (3+1/+1) of the following integrals? A Ов E + + + + 18 3+1+1 3++1 3++1 (A) √2×14 dx x+1 (C) 1½-½√ √ ² ( 14 ) d x (B) √31dx (D) So 3+x -dx is a Riemann sum approximation of which 5 (E) 1½√√3dx 2x+1arrow_forward2. Suppose the population of Wakanda t years after 2000 is given by the equation f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000 people? Show all your work, round your answer to two decimal places, and include units. (4 points)arrow_forward
- 3. Solve the equation, give the answer exactly (no calculator approximations), and show all your work. (4 points) log5 2x = 3arrow_forwardLet I = f(x) dx, where f is the function whose graph is shown. 4 2 y f X 1 2 3 4 (a) Use the graph to find L2, R2 and M2. R₂ M2 = = = (b) Are these underestimates or overestimates of I? O 42 is an underestimate. O 42 is an overestimate. ◇ R2 is an underestimate. OR2 is an overestimate. OM2 is an underestimate. ○ M2 is an overestimate. (c) Use the graph to find T2. T₂ =arrow_forwardVector u has a magnitude of 23 and vector v has a magnitude of 83. The angle between the two vectors is 126 degrees.a) Draw a fully-labelled vector diagram showing the two vectors and the resultant vector when they are added together.b) Find the magnitude of the resultant vector.c) Find the direction of the resultant vector relative to vector u. Solding by finding the x and y of the vectors and addingarrow_forward
- 3) If a is a positive number, what is the value of the following double integral? 2a Love Lv 2ay-y² .x2 + y2 dadyarrow_forward16. Solve each of the following equations for x. (a) 42x+1 = 64 (b) 27-3815 (c) 92. 27² = 3-1 (d) log x + log(x - 21) = 2 (e) 3 = 14 (f) 2x+1 = 51-2xarrow_forward11. Find the composition fog and gof for the following functions. 2 (a) f(x) = 2x+5, g(x) = x² 2 (b) f(x) = x²+x, g(x) = √√x 1 (c) f(x) = -1/2) 9 9(x) = х = - Xarrow_forward
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