Question

PLEASE HELP, WRONG/ABSURD ANSWERS GET REPORTED GOOD ANSWERS GET 25 POINTS AND BRAINLIEST!!
9.02

1. Find the limit of the function by using direct substitution.
limit as x approaches zero of quantity x squared minus six.

A) Does not exist
B) -6
C) 6
D) 0

2. Find the limit of the function by using direct substitution.
limit as x approaches three of quantity x squared plus eight x minus two.

A) 0
B) -31
C) Does not exist
D) 31

3. Find the limit of the function by using direct substitution.
limit as x approaches quantity pi divided by two of quantity two times e to the x times cosine of x.

A) 0
B) 1
C) two times e to the power of quantity pi divided by two.
D) pi divided by two.

4. Find the limit of the function algebraically.
limit as x approaches two of quantity x squared minus four divided by quantity x minus two.

A) 1
B) 4
C) 2
D) Does not exist

5. Find the limit of the function algebraically. 

Answer 1

Check the procedures in the picture attached.

1. Since we are using direct substitution, the only thing we need to do is replace $x$ by $6$ (the quantity $x$ is approaching to) in our quantity to get:
$x^{2} -6=0^{2} -6=-6$
We can conclude that the correct answer is B) -6

2. Again, since we are using direct substitution, th only thing we need to do is replace $x$ by $3$ (the quantity x is approaching to) to get:
$x^{2} +8x-2= 3^{2} +8(3)-2=9+24-2=31$
We can conclude that the correct answer is D) 31

3. Direct substitution again, so we are going to replace $x$ in our quantity by $\frac{ \pi }{2}$ to get:
$2e^{ \frac{ \pi }{2} } cos \frac{ \pi }{2}$
 And since cosine of $\frac{ \pi }{2}$ is 0, and any quantity multiplied by zero is zero:
$2e^{ \frac{ \pi }{2} } (0)=0$
We can conclude that the correct answer is A) 0

4. Here we need to so some algebra first. Notice that if we use direct substitution, the denominator will be zero, and we cannot divide by zero. So lets massage our quantity first:
$\frac{ x^{2} -4}{x-2} = \frac{ x^{2} - 2^{2} }{x-2} = \frac{(x-2)(x+2)}{x-2} =x+2$
Now, we can use direct substitution to get:
$x+2=2+2=4$
We can conclude that the correct answer is B) 4