Question

Find the value of c such that h(x) is continuous at x = 1 with the following function: h(x) = 5x² - x - 4 / (x - 1) if x ≠ 1, c if x = 1?

1) c = -3
2) c = -4
3) = -5
4) c = 0

Answer 1

The value of c such that h(x) is continuous at x = 1 is c = 25.

Step-by-step explanation:

To find the value of c such that h(x) is continuous at x = 1, we need to evaluate the limit of h(x) as x approaches 1.

When x ≠ 1, the function h(x) is given by h(x) = (5x² - x - 4) / (x - 1).

To evaluate the limit as x approaches 1, we substitute x = 1 in the function and simplify:

h(1) = (5(1)² - (1) - 4) / (1 - 1) = (5 - 1 - 4) / 0 = 0 / 0.

Since we have an indeterminate form of 0/0, we can try to simplify the expression further by factoring the numerator:

h(x) = (5x² - x - 4) / (x - 1) = (5(x - 1)(x + 4)) / (x - 1).

Cancel out the common factor of (x - 1), which gives h(x) = 5(x + 4).

Now, substitute x = 1 in the simplified expression:

h(1) = 5(1 + 4) = 5(5) = 25.

Therefore, the value of c such that h(x) is continuous at x = 1 is c = 25.