5. Assume f(x)= x. Evaluate %3D a. lim f(x). f. lim ((f(x))² – f(x)). g. lim ((f(x))³ + (f(x))² +2 · ƒ(x)). b. lim I+4 f(x) h. lim V3· (f(x))² + 4 · f(x). 1 c. lim 1+4 (f(x))²¯ (f(x))² – f(x) 5· f(x) d. lim -VF(r). i. lim e. lim V9. f(x). (f(r))² – 4ƒ(x) j. lim 4 (f(x))² + 4f(x)' I+4

Q: Use the graph to solve for z.* := lim f(r) 3 3 f(x) 2. 2.

A:

Q: lim xe-x

A: We have to evaluate the limit: limx→∞xe-x Rearranging the question using exponent rule a-m=1am,…

Q: b. Find lim (xv (xVx²+1-x²)

A:

Q: 2x+12 |x+6| If f(x)=- , determine whether lim f(x) exists. 44-6

A:

Q: If 2x - 2s f(x) sx² - 2x + 2 for x 2 0, find lim f(x). x-2

A:

Q: x* +x² – 1 limx→c x²+5

A:

Q: Use the graph of the function f(x) to answer each question . S(0) = (b) (c) (a) S(2) %3D S(3) = (d)…

A: The solution is given below in the next step: Looking closely at the graph following questions can…

Q: f(2 + h) – f(2) Find lim if f(x) = x + 7. h h→0 f(2 + h) – f(2) lim | (Simplify your answer.) h h→0

A: Here I am attaching image so that you understand each and every step.

Q: lim xV* = 1 x-0

A:

Q: 3. Consider the function f(x), whose graph is shown below. Determine the limit of a function, by…

A: The limit exists at a point means that ..... LHL left-hand limit of the function should be equal to…

Q: (c). lim 40+ (--) tanz

A: Limx-0+ (1/x)tanxFind the limit.

Q: If 3x − 5 ≤ f(x) ≤ x² − 3x + 4 for x ≥ 0, find_lim f(x). x →3

A: given  3x-5≤f(x)≤x2-3x+4for x≥0

Q: e- lim x-3 x2-9 V3x-3 ,x + 3

A:

Q: X 19. lim x→1x² + 4

A: To evaluate the following limit.

Q: If 2x – 2 < f(x) < x² – 2x + 2 for x 2 0, find lim f(x). X-2

A: The objective is to find the limit.

Q: Evaluate lim (tan-(t),e-2t,m²). t-1

A: We want to find given integral.

Q: B/ Find the value of lim,-.. 1. ²/2 O 1 O 2 7x²+x-100 2x²-5x N NIN

A: To evaluate: limx→∞7x2+x-1002x2-5x

Q: SX IF X <1 Let F(X) = (^(X-2) IF XZ1 a, Find Limx→1¹ and lim x⇒ F(x) b. does LIM X→1 f(x) exist? C,…

A:

Q: Find lim f(x). Im f0) -O x-2" X--2" (2.4) (4.3)

A: solution:-left hand limitlimx→2-f(x)=0

Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at the…

A:

Q: If lim x-4 x-2 f(x)-5 - =1, find lim f(x) X-4

A:

Q: 4x + 1 x + 5x a. lim 8x - x - 6 x ( 3x - 4) b. lim Зх + 9 3x 4x - 7 lim С.

A:

Q: If 2x – 2 0, find limf (x). x→1

A: We can use the sandwich theorem to solve this question.

Q: x*+x3 2. Calculate lim x→0 12x3+128

A: limx→∞x4+x312x3+128

Q: Show that lim (x³ - x) = 6 in the following steps. Do not use derivatives. x-2 (a) Show: if x - 2| <…

A:

Q: Inx 1 13. lim,

A: We will find the limit.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: