2.4.13 Find lim f(x) for the given function and value of c. xc 2x 8 7x f(x) c 8 2 X x+1 2x 8 7x lim 2 X x+1 x 8 (Type an integer or a simplified fraction.)

Q: 4 if x 2 Find the value of c such that lim f(x) exists. x→2

A: Given the piecewise function :

Q: 21. If f(x) = In x, then lim f (x) – f(3) is x→3 x – 3 1 (A) (B) e (C) In 3 (D) nonexistent

A: topic - limits

Q: 2.15 Suppose there exists a E R such that x > a implies f(x) > 0. Prove: 1 lim f(x) = 0 + lim 0. %3D…

A: We have to prove the given limit.

Q: 3x 15 if x 3° Compute the following or state that they do not exist. a) lim g(x) x-3- b) lim g(x)…

A: Please refer to the image below

Q: 3. Show that the largest value of o that can be used for some e > 0 if lim (2+ 5x) = 17 is エ→3 anx"…

A:

Q: In which limits below can we use L'Hospital's Rule? lim 818 Olim 848 Olim 48 Olim €8 et X In x e X H…

A:

Q: In evaluating S₂²² 2 dx 2 XV x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

A: We have to find the value of f(x) at given x.

Q: _15. What is lim f(x)? X-4 A. 0 В.1 С.2 D. Does Not Exist

A: Given: Following graph is given. To Find: 15. limx→4fx=?

Q: 6. Find the limit of f(x) = -- 10 as x approaches co and as x approaches - c lim f(x) = X00 (Type a…

A:

Q: 9. Given that limx→3 f(x) = 2 and limx→3 g(x) = −5 compute the following limits: (a) limx→3 2f(x)…

A: Given that limx→3f(x)=2 and limx→3g(x)=-5

Q: 6. Use the graph of the function f(x) = He to discuss the limit lim 40 f (x). 1+e!/x

A:

Q: _11. If lim (x² +1) = 2, and x = 2.5, then x->-1 lim (x² + 1) is equal to. x-2.5 A. 5.25 C. 6.25 B.…

A:

Q: ( 4, 0 < x < 4 1 5, 4 < x < 10 S 4, 0 < x < 4 x→4 5, 4 < x < 10 Use the graph of f(x) = to evaluate…

A:

Q: 4. Given there exists a function h(x) such that 2x³ + 5 < h(x) < xª + 5 for all r near 2, h(x) +3…

A:

Q: 3].. Use € Use e – 8 definition of a limit of function to show that: 2x = 1. x→1 1 + x a) lim X- b)…

A:

Q: II. Apply the limit laws on the following: lim (Vx/VA) 2. X+1 cos x x5+ lim X-3 3. X-1

A:

Q: 1. Find the following limits. e3r lim 3.x е (a) (b) lim e3/(2-a) lim In(1x2 - In(1 x (c) _ (d) lim…

A:

Q: 21. The cost of manufacturing a particular videotape (in dollars) is C(x)=15,000+ 45x , where x is…

A: cost function C(x)=15,000+45 x

Q: 14. Evaluate the following limits. (3-x+x2, 5x+1Y e) lim 2x y-0+ 5x-7 lim 2 f) X0o ( 3x2 x sin x lim…

A:

Q: Evaluate teh following fucntions

A: Dear Students,  “Since you have asked multiple questions in a single request, we will be answering…

Q: (7) ifa lim has a point that the equalio- prove PCz,y) is above L and only if 3x +2y >4

A:

Q: 9. Given that lim f(x) = 2 and lim g(x) = -5 compute the following limits: %3D (a) lim 2f(x) 3 (b)…

A:

Q: 6. Given the graph of g(x) below, evaluate lim (g(x)) x→4 -3- -2- 4 -1- DNE (does not exist) 4 -1…

A: Thats easy. Have a good day!!!

Q: 4. The graph of a function f(x) is shown at right. If g(x) = V1+ 3x , find lim [f(x) + 3 g(x)]. %3D…

A: The graph of the function fx is given. From that graph it is clear that, the function fx, at x=1…

Q: 1. Solve the following limits. (a) lim T→-∞ V1 + x² x In x (b) lim x UJ + x 00x 2+ sec (3x) (c) lim…

A:

Q: Q2/Give a value for each of the following limits: x2 - 4x – 21 1) lim 7 3x2 - 17x – 28 (7+2x)-V5-vZ)…

A:

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: The function values for h(x) near x = 3 are given in the table below. 2.90 2.95 2.99 3 3.01 3.05…

A: Given Ltx→3-hx=1.45         Ltx→3+hx=2.45         Ltx→3hx=2.45 From table

Q: The function values for h(x) near x = 1 are given in the table below. -0.10–0.05–0.011 2.01 2.05…

A: Given

Q: If 7- 4x s g(x) s7 cos x for all x, find lim g(x). lim g(x) = X-0 (Type an integer or a simplified…

A:

Q: 7. Compute the limit to infinity: 4-2+3r+1 a lim 7+3r-r+ 12

A:

Q: In evaluating 2dx E, is same as evaluating lim cos-¹(f(x)). Determine the value of f(x) if x=1.13…

A: Integration

Q: С. 1 Evaluate the following limits x2 +6x+5 1) lim x-5 x²+2x-15 x(х-5)-24 2) lim x→8 x2-8x (2+x)3-8…

A:

Q: 2. The limit of the following function equals: x2/3 + x-1 lim x--00 x2/3 + cos2 x

A:

Q: Q.2 Show that r(ax) _ 1 lim x0 (x)

A: to show  limx→0ΓaxΓx=1a   ...i as we know Γn=Γn+1n using this formula we get Γx=Γx+1xΓax=Γax+1ax

Q: 3. Consider the function f defined below. Inx for 0<xs2 If f(x)={ then lim f(x) is **]x²In 2 for 2…

A: Given:  fx=lnx         for 0&lt;x≤2x2 ln2     for 2&lt;x≤4limx→2 fx=?

Q: 1. Show that for all f e L'(R) lim

A: To show: limδ→1∫f(x)-fxδdx=0 Concept used: ∫fxdx=Fx+c Chain rule: ∫fxadx=1aFx+c

Q: Please I want solution of sub-parts question 5 with step by step. Many Thanks

A:

Q: 3. Find the following limits: x7 a) lim x→∞ In x x4 b) lim x→∞ e* 11x²+55x c) lim x→∞ 3.5x²+7777

A:

Q: 6 Evaluate the limits lim: X+ co X 6.

A: Topic:-   limits and continuity

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: Can i get help with this problem step by step?

A: Calculation:

Q: 4 6.xy1 Find lim if it exists. (x,y)→(0,0) x² + y8 *

A:

Q: 4. Evaluate the following limits: sin x (a) lim x-0 x³-7x2+10x (b) lim x→2 x2+x-6 sin at (c) lim…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: 2. Complete the table by computing f(x) at the given values of x, accurate to five decimal places.…

A:

Q: 4x 7 lim 1+ Compute the limit: x→0

A: here we put value of limit then we calculate

Q: 16) [5] Compute the value of the following limits using L'Hôpital's Rule: Ax -1-4x a) lim x40…

A:

Q: 9. Consider the following information about the graph of a continuous function m(x): • lim→-0 m(x) =…

A: Given: The function mx is a continuous function limx→-∞mx=-2 and limx→∞mx=2 The sign of m' and m''…

Q: -12 -10 -8 -6 -4 -2. 4 10 12 nd i) lim f(x) ii) lim f(x) iii) lim f(x) iv) f(-8) X-2 %65 t m

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: Suppose we define h(x) to be a function in which 12 0 is small (in other words, when x is slightly…

A: We have the given inequality for h(x) in 3+ domain. Using this we have to find the limit x ➡️ 3+…