Find the indicated one sided limits of f.
f(x)= (x^2+8)/(x^2-25)
what is the limit as x goes to -5+(from the right side)?
What is the limit as x goes to 5+(from the right side?
if x = -4.99
f = -329
if x = -4.999
f = -3299
negative infinity
numerator --> 33
denominator ---> - 0 because x^2 always < 25
opposite for x>5 by a little
---> + oo
To find the indicated one-sided limits of a function, we evaluate the function as x approaches the given value from the specified side.
For the function f(x) = (x^2 + 8) / (x^2 - 25), let's find the limits as x approaches -5 (from the right side) and 5 (from the right side).
1. Limit as x approaches -5 from the right side:
To find this limit, we substitute x = -5 into the function. However, we need to approach -5 from the right side, which means x should be slightly greater than -5. Let's use x = -4.9, for example.
f(-4.9) = ((-4.9)^2 + 8) / ((-4.9)^2 - 25) ≈ (24.01 + 8) / (24.01 - 25) ≈ 32.01 / -0.99 ≈ -32.33
So, the limit of f(x) as x approaches -5 from the right side (x → -5+) is approximately -32.33.
2. Limit as x approaches 5 from the right side:
Similarly, we substitute x = 5 into the function, approaching from the right side where x is slightly greater than 5. Let's use x = 5.1, for instance.
f(5.1) = ((5.1)^2 + 8) / ((5.1)^2 - 25) ≈ (26.01 + 8) / (26.01 - 25) ≈ 34.01 / 1.01 ≈ 33.67
So, the limit of f(x) as x approaches 5 from the right side (x → 5+) is approximately 33.67.