Evaluate the following limits. If necessary, change the form of the function.
a) lim x -> 1 = (x^2 - 3x +5)/(x-2)
=(x^2 - 3x +5)/(x-2)
=(1^2 - (3(1)+5)/(1-2)
= -3
b) lim x-> 0 = (4x-5x^2)/x
=(4x-5x^2)/x
=x(4-5x)/x
=4-5x
=4-5(0)
=4
can someone see if my answers correct?
a) your answer is correct, but you have an extra paren in lin e 3.
(1^2 - (3(1)+5)/(1-2)
should be
(1^2 - 3(1) + 5)/(1-2)
b) is also correct
To evaluate limits, you need to find the value that a function approaches as it gets arbitrarily close to a specific value or approaches infinity or negative infinity. Let's check your answers.
a) To evaluate the limit of (x^2 - 3x + 5)/(x - 2) as x approaches 1, first substitute x = 1 into the expression:
lim x->1 [(x^2 - 3x + 5)/(x - 2)] = (1^2 - 3(1) + 5)/(1 - 2) = (1 - 3 + 5)/(-1) = 3/(-1) = -3
Your answer for part a) is correct.
b) To evaluate the limit of (4x - 5x^2)/x as x approaches 0, again substitute x = 0 into the expression:
lim x->0 [(4x - 5x^2)/x] = (4(0) - 5(0^2))/(0) = 0/0
Here we encounter an indeterminate form (0/0), which means we can't directly evaluate the limit using algebraic manipulation. To proceed, we can try factoring out x from the numerator:
lim x->0 [(4x - 5x^2)/x] = lim x->0 [x(4 - 5x)/x] = lim x->0 (4 - 5x)
Now, we can substitute x = 0 into the expression:
lim x->0 (4 - 5x) = 4 - 5(0) = 4
So, your answer for part b) is also correct.