Graph the logarithmic function y=log(x-4) please show work
1 answer:
Answer:
Graph shows the vertical asymptote at x nearing 4.
Explanation:X must be more than 4 otherwise log(x-4) will be invalid;
Let us make a table of x & y
<span>x→→<span>log<span>(x−4)</span></span></span>
------- ----------------
<span>5→→0</span>
<span>9→→.7</span>
<span>14→→1</span>
<span>19→→1.18</span>
<span>24→→1.30</span>
Now we can plot the Graph with the value of x and y. On this Graph Vertical asymptote is at x nearing the value 4. (Graph Below)
Hope this helped :)
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<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units
<u>Solution-</u>
As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with
x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)
Then, substituting these values in the plane equation to get the z parameter,
cos t + 2sin t + z = 2
⇒ z = 2 - cos t - 2sin t
∴
As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π
∴ Arc length
Now evaluating the integral using calculator,
