f(2) = 1, f(-1) = 0, lim f(x) = 0, lim f(x) = o0, %3D %3D lim f(x) -00, and lim f(x) = 1 =

Q: lim x→-0.5- Vx + 1

A:

Q: 2x*-3x+2x2-x+1 lim -6x-x2+x+2 1 3 O O

A:

Q: 10x5/3 – x1/3 +8 - (c) lim x→00 x8/5 + 2x + 15/x Σ 10Va – 13x + 2 (d) lim x-0 5x + 15x2/3 Σ || – 12

A: We have to solve

Q: ー2 a) lim X >6 (x-6)3 b) lim E) ゼ+t

A:

Q: x' +4 a. lim X-4 x-2 %3D x² -1 b. lim- xl x' -1 Vx - Ja lim- с. х —а

A: topic - limits

Q: Evalugte lim(3x-1)/x Xー>○ X/2

A: The solution is :

Q: lim x approaches -3  x + 3 /[x2 + 4x + 3]

A: Given: limx→-3x+3x2+4x+3 Apply the limits. limx→-3x+3x2+4x+3=-3+3-32+4(-3)+3=09-12+3=00 As, it…

Q: Evaluode Lim [x]+[2x ]+ n2

A: We know that, x-1<x≤x Therefore, 2x-1<2x≤2x ⇒3x-1<3x≤3x . . . ⇒nx-1<nx≤nx ∴ (x + 2x + 3x…

Q: lim f(x) = %3D x-8-

A: We can clearly see from the graph that, f(x) is discontinous at  x = -8  But, if we move slightly…

Q: Determine the following limits or state that they do not exist.

A: Given f(x)=x-4x(x+2)

Q: (a) lim sih 7x (b) lim x 0 sin 7x x - 9 (c) lim x-9 x - 3

A:

Q: (a) lim n-0 2 – ni x² – 4 (b) lim x + 4 x² – 4 (c) lim x – 2

A:

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

A:

Q: (e) limVx ) lim -+(-1)") X-00 n→0 n n²-12345 x2 +9 (g) lim n +1 (h) lim x∞x3 +1

A:

Q: limy 2 X- 2

A: Here we have to evaluate limx→21x-12x-2

Q: x - 25 (a) limx→o х2 — 4х — 5 х2 — 25 (b) limx¬5 х2 — 4х — 5 x4 + 5x3 + 6x2 (c) limx→-2 x²(x + 1) –…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2-x x+²√√x+2-√√3x-2 c) lim-

A:

Q: 5. lim -0.01 -0.001 -0.0001 0.0001 0.001 0.01 f(x) x-4 : lim x0x2 - 16 Mel

A: To complete the table and make the graph

Q: i) f'(2) = 0 and f" (2) < 0 ii) lim-0 16+h)-15) iii) lim, +x f(x) = 2 iv) f(0) = -2 v) lim, 40 f(x)…

A: We can use the concept of function in order to solve the given application of derivative is also…

Q: 2x -5x +2 3. Calculate the limit lim .2 x-2x X→2 X -3x +4

A: Limit of the function f(x) as x approaches  to a means as x approaches to a from left side and right…

Q: Find the limits in Exercise

A: limx22-1x

Q: (x² - 3) Build a table to estimate lim x-0 sin x

A: Given expression is

Q: valuate 10-Vx a. lim x→100 x-100 b. lim (-2x+4)²–4 1 c. lim *+2 5 x→3 x-3 X-3 3-x

A: Given that:

Q: limx->0+ (x^(e) -5x^(4) -3x^(6) - x^(3) +100)

A:

Q: eim 2メー5 メ4 -2 z lim Vx+4-1-x-2 メ→ メ+3 lim 2-X Z-メ 24メ

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: x-2x x (水) 3t-4 t- lim 4-t

A:

Q: X. lim (3x – x -3 - 2) (2x² +4x+5) K. lim x+1 2x2+2x-4 Z. lim x-1 x-1 a. lim (+3) а. N. lim – (-16)

A: We will find the limits as shown below

Q: aterminate form, use factor 2-1 1. lim X14x+4 +2x-15 2. lim I-3 x+4x-21 x+x-20 3. lim X-4 r-64

A:

Q: x² – 4x lim +-1 г2 — 3х — 4 I-1 x

A: Limit does not exist Explanation is given below...

Q: 1. lim )Gt h->0 2. lim xZ X-1 X>( X-I

A: here is the solution

Q: lim ecos x = x→0

A:

Q: 8- 6- y = h(x) y = h(x) -4 -3 2 -2- 2. lim, h(x): 3. lim,→2- h(x): 4. lim,-2+ h(x): 5. limy-2 h(x):…

A: Find the following value from the graph:

Q: x- 2 5. Evaluate lim- 1→2 Jx+2 - 2 Solution:

A:

Q: Use the limit properties to find the following limit.

A: Given that, limx→3fx=3      ...(1)limx→3gx=2      ...(2)

Q: 1 + (a) Lim X-1 'x+1, -2

A:

Q: Find the limits

A: Given as L=limx→∞x2+x-x2-x

Q: lim (2a +x) X-

A: We find the limit by substitution

Q: Jx-2 %3D F(x) x²+x-6 Does lim F(x) exist? x-2

A:

Q: x - y 1. lim (x,y)¬(3,3) 1 2. lim x-0 xVx + 1

A: (1)  lim(x,y)→(3,3)x-yx-y=lim(x,y)→(3,3)x-yx-y×x+yx+y (We rationalize the denominator)…

Q: g) Y2-Y1 X2-X1 h) f(x+h)-f(x) (x+h)-x i) lim-0 f(x+h)-f(x) (x+h)-x i) lim-0 f(x+h)-f(x) (x+h)+x

A:

Q: x² - 5x – 24 lim Calculate the limit: x-3 x+3

A: the given limit is: limx→-3x2-5x-24x+3 we have to evaluate the given limit.

Q: lim-o f(x+h)-f(x) 1) Given f(x) = x2-3 find 5x+2x2+1 2) limx-ox3+3x

A: 1 We have to find limh→0fx+h-fxh for the given function fx=x2-3. 2 We have to find the limit…

Q: (x² - 3) 7. Build a table to estimate lim sin x

A:

Q: Find the limits

A: Find the limits

Q: Let h(x)

A: Consider the given function and its graph as hx=x2   x&lt;23x=22x&gt;2

Q: Question 1 Vx-2 x->4 x-16 i. lim ii. lim lx-5 1 x->2 x+x-25 iii) lim (Vx +x - x) X->00

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: lim %3D X2 -マメ

A: The solution for the above question is as shown below.

Q: 2 ] (d) lim x-1Lx-1 x2 -1

A: Topic = Limits