Complete the table by computing f(x) at the given values of x. (Round your answers to three decimal places.)
f(x) = 2x^2 - 7
x 6.9 6.99 6.999 7.001 7.01 7.1
Use these results to estimate the indicated limit (if it exists). (If an answer does not exist, enter DNE.)
lim_(x->7)f(x)
Complete the table by computing f(x) at the given values of x. (Round your answers to three decimal places.)
f(x) =
|x − 10|
x − 10
To complete the table, we need to substitute the given values of x into the function f(x) = 2x^2 - 7.
For x = 6.9:
f(6.9) = 2(6.9)^2 - 7 = 2(47.61) - 7 = 95.22 - 7 = 88.22
For x = 6.99:
f(6.99) = 2(6.99)^2 - 7 = 2(48.8601) - 7 = 97.7202 - 7 = 90.7202
For x = 6.999:
f(6.999) = 2(6.999)^2 - 7 = 2(48.993001) - 7 = 97.986002 - 7 = 90.986002
For x = 7.001:
f(7.001) = 2(7.001)^2 - 7 = 2(49.014001) - 7 = 98.028002 - 7 = 91.028002
For x = 7.01:
f(7.01) = 2(7.01)^2 - 7 = 2(49.1401) - 7 = 98.2802 - 7 = 91.2802
For x = 7.1:
f(7.1) = 2(7.1)^2 - 7 = 2(50.41) - 7 = 100.82 - 7 = 93.82
Now, to estimate the limit as x approaches 7 (lim_(x->7)f(x)), we look at the values of f(x) as x gets closer to 7.
From the table, we can see that as x approaches 7, f(x) approaches 91.028002. Therefore, we can estimate that the limit as x approaches 7 of f(x) is 91.028002.