f(x) – 5 - a. If lim 3, find lim f(x). х>2 х — 2 - 2 x→2 f(x) – 5 b. If lim x→2 X – 2 4, find lim f(x). x→2

Q: If f(x)=2-3x². O a. O b. O c. lim h→0 lim h→0 lim 30 From first principles select the correct step.…

A: Given :fx=2-3x2

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A:

Q: 1- V1– x2 с) lim x→0 [without using l'Hospital Rule] x2 -1- x – a? d lim x→0

A:

Q: Find the limit (if it exist)

A: Given:

Q: Given: limx→+∞ f(x)=4 limx→+∞ g(x)=3 limx→+∞ h(x)=-7 Find: limx→+∞ [f(x)+3g(x)] = ? limx→+∞…

A:

Q: 3-Vx+3 6. (10) Find lim analytically (if it exists). X→6 X-6

A:

Q: -xy lim (x,y)→(0,0) x²+y2

A:

Q: 2) IF f(x) = {" (x + 2 , – 1<x<0 x, 0<x< 1 find limf(x) %3D

A: To find lim(x tends to inf) f(x)

Q: b) Find two functions such that lim, 0 f(x) = 0 lim, 0 g(x) = 0 but lim, 0 f(x)g(x) = 1

A:

Q: Using the definition of the derivative, find f'(x). Then find f'(-3), f'(0), and f'(4) when the…

A: f(x)=2x3+10

Q: 16. Find the equation of the line tangent to the functionf (x) = 6Vx at x-4. *hint: use lim,a…

A:

Q: 3 k3 -ル+} (my)0, t) 4 +n -y lim

A: Given that  Limit

Q: Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=

A: Given:  limh→0 5ex-5ex+h3h   Basic concept: The definition of the first principle of the…

Q: a. Find the Domain for y = = /4 -x + ! b. For what value of (k) is the function y-f(x) continuous at…

A:

Q: 2x+1 if x 2 Determine the one-sided limit lim f(x). x-2- 2

A: The given function is:

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: 1+t-V1-t lim

A: To evaluate: limt→01+t-1-tt   if we substitute t=0, we get 00 (indeterminate form)   Consider…

Q: Find Lim-0.0 (r² + y²) In(x² +y²) '(xy)(0,0)

A:

Q: Vx- 2 4. lim- x-2 x2 - 4 y-1 5. lim- Vy? +3 – 2

A: We can apply the limit to the expression by applying the limit as value for the variable in the…

Q: + h 4 (a) Lim×-1'x+1 X (b) Lim h→0 V5h + 4 – 2 -2 - t3 – 1 3. (c) Lim t-1 t-1 II

A: To show the given limits, we use the algebraic indentity and rationalization of a fraction.

Q: Let h(x)

A: hx=x2,      x&lt;23,       x=22,       x&gt;2 Now, The left hand limit at x=2 is,…

Q: 3. Find the indicated limits. if x 2 f(x) -2+ 4x – x² a) lim f(x) x→2+ b) lim f(x) x→2- c) lim f…

A:

Q: (a) lim x→2 arctan(7-3x)-" 2х-4 4 (b) 10-e5x lim x→00 16-x2

A: See the calculation and explanation below

Q: Q.4: Prove or disprove, lim f(x) = 4 If f(x) = x # 2 x = 2' I-2

A:

Q: lim is x-0 X O A. 0 О в. 1 C. 8.

A: B. 1

Q: 1. Consider the function f(x, y) = 2y (a) Show that lim (x,y)(0,0) f(x, y) does not exist by using…

A: Note: if a limit exists at a point,it must be the same limit along any path approaching that point.…

Q: I if X > 4 and J (X). 4X + 1 i1 X<4. Find lim f(x) x→4+

A: Given; f(x)=√x-1 if x&gt;4 and f(x)=x2-4x+1 if x&lt;4.

Q: 2. Consider the function: + 3 if x 2 %3D 17 if x = 2. %3D Find lim, 2 f(x).

A: Function given is- f(x)=x2+3       if x&lt;2x3-1      if x&gt;217           if x=2  To find…

Q: 8-3x, for x <1 For parts b) and c), let f(x)= %3D x+x, for x21' b) lim f(x) x→1

A: We have to evaluate  limx→1- f(x) For x &lt;1 , f(x) = 8 - 3x

Q: 1/x, if x – 1 С. 1/x, if x – 1[ %3D X- -1

A: c) f(x) = 1/xx≤-1x2-2x&gt;-1limx→0f(x) = limx→0(x2-2) = 02-2 = 0-2 = -2

Q: z² +et= 1-400 2z-e² 2* - 3* 17. lim- x-0 18. lim cotxln(x+1) x-0 16. lim-

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: y of -4 -2 -2 (a) (1) (b) lim f(x) x-1 2.

A:

Q: x2-x-2 2x-4 2sin(6x–12) 3(x-2) Sx-1 Let f(x)* ,g(x) • and h(x) Vz+2+1 a. Find lim f(x), lim g(x),…

A:

Q: x' + 2, if x 0 (a) Find lim f(x).

A: Since , the only point of discontinuity can be zero . For rest of the points on ℝ the function is…

Q: 4. Given that f(x)=4x - 3 f (1+h)- ƒ(1) Find lim ,x21

A: Given query is to find the value of indicated operation.

Q: your a ;) lim x4+メーLo メ→。 i) lim 左十 \im tメーLo X→-∞ iii) \m 4a(a+)しメー2)しメ+ム) メ→ ○

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). a. Make a table of the values of h at x = 2.9, 2.99, 2.999,…

A: First, we factor numerator and denominator. Then we simplify for x not equal to 3. Then use this…

Q: f(x)=(1-2x)/x, find lim f(x) approaches 3 and limit f(x) approaches 4

A: Given that the function is,

Q: 5x b) lim lim-0 2ln(x+1) ex-e-x c) lim lim-0 2x x2-2x-3 d) lim lim-3 x-5x+6

A:

Q: - [x² + 2 if x < 2 (x) l(x - 3)2 if x 2 2 (a) Find the following limits. (If an answer does not…

A: Given function:

Q: x4/7 – 1 lim f'(a) where x→-1 x + 1 f(x) = and a = x4/7 lim x + 1 1 х>-1 II

A: Explanation of the solution is given below...

Q: x+1 If f(x) = Solve to find lim f(x)? %3D Vx2+5-x'

A: Here is complete computation for your limit

Q: S -2x? + 5x 7x² – 5 for x 0. According to the alternate form of the definition of the derivative,…

A: Given:

Q: 3x +x 6. Evaluate the limit: lim- x→0 а. О С. 1 b. 3 d. -1

A: “Since you have asked multiple questions, we will solve ONE question for you. If you want any…

Q: x+1 If f (x) : Solve to find lim f(x)? Vx2+5-x'

A: We find limit

Q: Consider the function - x2, x+1 f(x) = 2, x = 1 O Graph the function f(x). O Find lim,1-f(x) and…

A:

Q: 1. Prove using e-d definition. (d) lim (4x + 3) = 7 x→1 x2 – 9 = 6 - (e) lim x→3 x – 3

A: To prove the limit using epsilon-delta definition

Q: x³y Find the limit lim , if it exists. (x.y)-(0,0) x²+y2

A:

Q: Find the limit of f(x) = 6 - 2 as x approaches o and as x approaches - o. lim f(x) = %3D (Type a…

A: