PLEASE HELP ASAP, GOOD ANSWERS GET BRAINLIEST +50 POINTS!! WRONG ANSWERS GET REPORTED.9.061. Find the derivative of f(x) = -4x2 + 11x at x = 10. A) -19.5B) -69C) 30D) -3002. Find the derivative of f(x) = 8x + 4 at x = 9. A) 0B) 4C) 8D) 93. Find the derivative of f(x) = 4 divided by x at x = 2. A) -4B) -1C) 1D) 44. Find the derivative of f(x) = negative 9 divided by x at x = -4. A) 4 divided by 9B) 16 divided by 9C) 9 divided by 16D) 9 divided by 45. Find the limit of the function by using direct substitution.limit as x approaches zero of quantity x squared plus five.A) Does not existB) -5C) 0D) 56. Find the limit of the function by using direct substitution.limit as x approaches four of quantity x squared plus three x minus oneA) Does not existB) -27C) 0D) 277. Find the limit of the function algebraically.limit as x approaches four of quantity x squared minus sixteen divided by quantity x minus four.A) Does not existB) 4C) 1D) 88. Find the limit of the function algebraically. limit as x approaches zero of quantity x squared minus two x divided by x to the fourth power.A) Does not existB) 8C) 0D) -89. Use the given graph to determine the limit, if it exists.A coordinate graph is shown with a horizontal line crossing the y axis at four that ends at the open point 2, 4, a closed point at 2, 1, and another horizontal line starting at the open point 2, negative 3.Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x. A) -3; 4B) 1; 1C) 4; -3D) Does not exist; does not exist10. Use the given graph to determine the limit, if it exists.A coordinate graph is shown with a downward sloped line crossing the y axis at the origin that ends at the open point 3, negative 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, negative 4.Find limit as x approaches three from the right of f of x. .A) -1B) 7C) -4D) Does not exist11. Find the indicated limit, if it exists. limit of f of x as x approaches negative 1 where f of x equals x plus 1 when x is less than negative 1 and f of x equals 1 minus x when x is greater than or equal to negative 1A) -1B) 2C) The limit does not exist.D) 012. Find the indicated limit, if it exists. limit of f of x as x approaches 0 where f of x equals 7 minus x squared when x is less than 0, 7 when x equals 0, and negative 10 x plus 7 when x is greater than 0A) The limit does not exist.B) 7C) -10D) -1713. Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 3 as x approaches 3 from the left.A) ∞; x = -3B) -∞; x = -3C) -∞; x = 3D) 1 ; no vertical asymptotes14. The position of an object at time t is given by s(t) = -1 - 13t. Find the instantaneous velocity at t = 8 by finding the derivative.15. Use graphs and tables to find the limit and identify any vertical asymptotes of the function. limit of 1 divided by the quantity x minus 1 squared as x approaches 1

(1) Ans: Option (B) -69

Given function: [tex]f(x) = -4x^2 + 11x[/tex]

The derivative of f(x) with respect to x is:

[tex] \frac{df}{dx} = -4 * 2x + 11 [/tex] --- (1)

Plug the value of x = 10 in (1)

(1) => [tex]\frac{df}{dx} |_{x=10} = -4 * 2(10) + 11 = -69[/tex]

Hence the correct answer is Option (B) -69

(2)  Ans: Option (C) 8

Given function: [tex]f(x) = 8x + 4[/tex]

The derivative of f(x) with respect to x is:

[tex] \frac{df}{dx} = 8 [/tex] --- (1)

Plug the value of x = 9 in (1)

(1) => [tex]\frac{df}{dx} |_{x=9} = 8[/tex]

Hence the correct answer is Option (C) 8

(3)  Ans: Option (B) -1.

Given function: [tex]f(x) = \frac{4}{x} [/tex] 

The derivative of f(x) with respect to x is:
[tex] \frac{df}{dx} = \frac{d}{dx}(4x^{-1}) [/tex]
[tex]\frac{df}{dx} = 4 * -1 * x^{-1 -1} \\ \frac{df}{dx} = -4 * x^{-2} [/tex]

At x = 2:
[tex]\frac{df}{dx} |_{x=2} = -4 * (2)^{-2} = -1[/tex]

Hence the correct answer is Option (B) -1.

(4) Ans: Option (C) 9 divided by 16.
Given function: [tex]f(x) = \frac{-9}{x} [/tex] 

The derivative of f(x) with respect to x is:
[tex] \frac{df}{dx} = \frac{d}{dx}(-9x^{-1}) [/tex]
[tex]\frac{df}{dx} = -4 * -1 * x^{-1 -1} \\ \frac{df}{dx} = 9 * x^{-2} [/tex]

At x = -4:
[tex]\frac{df}{dx} |_{x=-4} = 9 * (-4)^{-2} =  \frac{9}{16}  [/tex]

Hence the correct answer is Option (C) 9 divided by 16.

(5) Ans: Option (D) 5

Given function:
[tex]f(x) = x^2 + 5 [/tex]

Now apply the limit:
[tex] \lim_{x \to 0} f(x) = \lim_{x \to 0} (x^2 + 5) \\ \lim_{x \to 0} f(x) = 0^2 + 5\\ \lim_{x \to 0} f(x) = 5[/tex]

The correct answer is Option (D) 5.

(6) Ans: Option (D) 27

Given function:
[tex]f(x) = x^2 + 3x - 1[/tex]

Apply the limit:
[tex] \lim_{x \to 4} f(x) = \lim_{x \to 4} (x^2 + 3x - 1) \\ \lim_{x \to 4} f(x) = (4)^2 + 3(4) -1 = 27[/tex]

The correct option is (D) 27

(7) Ans: Option (D) 8.

Given function:
[tex]f(x) = \frac{x^2 - 16}{x-4} [/tex]

[tex]f(x) = \frac{x^2 - 16}{x-4} \\ f(x) = \frac{(x+4)(x-4)}{(x-4)} \\ f(x) = x+4 [/tex]

Now apply limit:
[tex] \lim_{x \to 4} f(x) = \lim_{x \to 4} (x + 4) = 4+4 = 8[/tex]

The correct option is (D) 8.

(8) Ans: Option (A) Does not exist.

Given function:
[tex]f(x) = \frac{x^2 - 2x}{x^4} = \frac{x(x-2)}{x^4} = \frac{x-2}{x^3} [/tex]
Apply limit:
[tex] \lim_{x \to 0} f(x) = \lim_{x \to 0} \frac{x-2}{x^3} = \frac{-2}{0^3} = -\infty [/tex]

The correct answer is (A) Does not exist.

(9),(10)
Please attach the graphs! Thanks! :)

(11) Ans: limit doesn't exist (Option C)
Given function:
[tex]f(x) = \left \{ {{x+1~~~~~x\ \textless \ -1} \atop {1-x~~~~~x\geq -1}} \right. [/tex]

If both sides are equal on applying limit then limit does exist.

Let check:
If x<-1: answer would be -1+1 = 0
If x≥-1: answer would be 1-(-1) =2

Since both are not equal, as 0≠2, hence limit doesn't exist (Option C).

(12) Ans: Option (B) 7.

Given function:
[tex]f(x) = \left \{ {{7-x^2~~~~~x\ \textless \ 0} \atop {-10x+7~~~~~x\textgreater 0}} \right. \\ and \\ f(x) = 7~~~~~~~x=0 [/tex]

If all of above three are equal upon applying limit, then limit exists.

When x < 0 -> 7-(0)^2 = 7
When x = 0 -> 7
When x > 0 -> -10(0) + 7 = 7

ALL of the THREE must be equal. As they are equal. Hence the correct option is (B) 7.

(13) Ans: -∞,  x =3 (Option C)

Given function:
f(x) = 1/(x-3).
Table:
x                      f(x)=1/(x-3)       
----------------------------------------
2.9                       -10
2.99                     -100
2.999                   -1000
2.9999                 -10000
3.0                        -∞

Below the graph is attached! As you can see in the graph that at x=3, the curve approaches but NEVER exactly touches the x=3 line. Also the curve is in downward direction when you approach from the left. Hence, -∞,  x =3 (Option C)

(14) Ans: Inst. velocity = -13

Given function:
s(t) = -1 -13t
Instantaneous velocity = [tex] \frac{ds(t)}{dt} [/tex]
Therefore,
[tex]\frac{ds(t)}{dt} = \frac{d}{dt} (-1-13t) = -13 [/tex]

At t=8:
Inst. velocity = -13

(15) Ans: +∞,  x =1

Given function:
f(x) = 1/(x-1)^2
Table:
x              f(x)= 1/(x-1)^2   
----------------------------------
0.9             +100
0.99           +10000
0.999         +1000000
0.9999       +100000000
1.0              +∞

Below the graph is attached! As you can see in the graph that at x=1, the curve approaches but NEVER exactly touches the x=1 line. The curve is in upward direction if approached from left or right. Hence, the correct answer is: +∞,  x =1