I need all working and steps to be shown. AlsoI need a need step by step process how how you arrived at the answer and explanations ( espically for the graphs). Everything should be clear. Document...

I need all working and steps to be shown.

AlsoI need a need step by step process how how you arrived at the answer and explanations ( espically for the graphs).

Everything should be clear.

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MAC 223 XXXXXXXXXXTest Chapters 1 and 2 XXXXXXXXXXName___________________________________A. Goldstein XXXXXXXXXX5 points eachDecide whether the limit exists. If it exists, find its value.1) Find 1)a. lim f(x) XXXXXXXXXXb. lim f(x) XXXXXXXXXXc. lim f(x)- + x 0x 0 x 0Find the limit, if it exists.2x - 92) lim 2)x- 3x 33) Find the limit, if it exists. 3)x- 4limx- 2x 412x + 4, for x<>

Solution

David answered on Dec 20 2021
1) Solution:
a.

( )
It is the value of the function just before 0.
.

( )
It is the value of the function just after 0.
c.

( )
It is the value of the function exactly at 0.
Now, since

( )

( )
i.e. Left hand limit is not equal to right hand limit, the limit for the given function does not
exist at 0.
2) Solution:

( )( )

( )
Now,
LHL:

( )
RHL:

( )
Since, LHL = RHL
Limit exists and is equal to 6.
3) Solution:

(√ )

(√ )(√ )

(√ )
Now,
LHL:

(√ )
RHL:

(√ )
Since, LHL = RHL
Limit exists and is equal to 4.
4) Solution:
( ) {

For a function to be continuous at a point ,

( )

( )

( )
i.e. the LHL, RHL and value of function at the exact point should be same.
Now, at
LHL:

( )

( )

( )
( )
Since,
( ) is not continuous at
5) Solution:
From the definition of derivative
( )

( ) ( )

Now,
( )
( )

( )

( )

( )

( )
6) Solution:
( )

The slope of the tangent to any point at the given curve is the derivative ( )
( )

Now,
To find the equation of tangent at point ( )...
SOLUTION.PDF