Question

Lim(x->1) (2x^2+5x-7)/(7x^2-3x-4)

Answer 1

= 228)))))))))))lhdhxhzff

Answer 2

To find the limit of the given function as x approaches 1, we can directly substitute x = 1 into the expression. However, since this would result in division by zero in the denominator, we should try to simplify the expression first.

Given function: f(x) = (2x^2 + 5x - 7) / (7x^2 - 3x - 4)

Step 1: Factorize the numerator and denominator. Numerator: 2x^2 + 5x - 7 Denominator: 7x^2 - 3x - 4

The numerator does not factor further, but the denominator can be factorized as follows: Denominator: (7x + 8)(x - 1)

Step 2: Cancel out common factors if possible. Now, the (x - 1) term appears in both the numerator and the denominator, so we can cancel it out.

f(x) = (2x^2 + 5x - 7) / (7x^2 - 3x - 4) f(x) = (2x^2 + 5x - 7) / [(7x + 8)(x - 1)] f(x) = [(2x + 7)(x - 1)] / [(7x + 8)(x - 1)]

Step 3: Cancel the common factor (x - 1) from the numerator and denominator. f(x) = (2x + 7) / (7x + 8)

Step 4: Now, we can find the limit as x approaches 1 by directly substituting x = 1 into the simplified expression.

lim(x->1) f(x) = lim(x->1) (2x + 7) / (7x + 8)

Now, we can substitute x = 1:

lim(x->1) f(x) = (2 * 1 + 7) / (7 * 1 + 8) lim(x->1) f(x) = (2 + 7) / (7 + 8) lim(x->1) f(x) = 9 / 15

Step 5: Simplify the fraction.

lim(x->1) f(x) = 3 / 5

Therefore, the limit of the given function as x approaches 1 is 3/5.