Let Find the value of k that will make f continuous on
A)3
B)28
C)-2

Question

Let  Find the value of k that will make f continuous on 
A)3 
B)28 
C)-2

Quizplus · Accepted Answer

In order for f to be continuous, we need to ensure that the function is continuous at the point 11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00. To do so, we need to find the limit of f as it approaches this point from both directions:
lim(x->11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00+) f(x) = lim(x->11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00+) (5x + k)
= 5(11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00) + k
= 560e07d3_3a9c_7bdf_d2d1_cea0a6b92e49 + k

lim(x->11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00-) f(x) = lim(x->11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00-) (x^2 - 2)
= (11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00)^2 - 2
= 12cc7583_bf3e_b6e8_cf1f_c3e3f52acf3d

For f to be continuous at the given point, these two limits must be equal. Therefore, we have:

560e07d3_3a9c_7bdf_d2d1_cea0a6b92e49 + k = 12cc7583_bf3e_b6e8_cf1f_c3e3f52acf3d

Solving for k, we get:

k = 12cc7583_bf3e_b6e8_cf1f_c3e3f52acf3d - 560e07d3_3a9c_7bdf_d2d1_cea0a6b92e49
k = 2f2c
k = 3 (in decimal)

Therefore, the best choice is A) 3.

Let Find the Value of K That Will Make