lim f(x)= a. %3D b. lim f(x) = %3D x-4 c. f(4) = %3D

Q: d. Lim (1-3x)^5/x

A: The answer is - 1/e15

Q: Give precise definitions of the following statements.

A:

Q: 8. (x - 1) dx √x lim

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: Find the limit (if it exist)

A: Given:

Q: c. lim f(x) X→-2+ d. lim f(x) X-0

A:

Q: Find the limit.

A:

Q: e²x-2x-1 x² f(x) = a) lim f(x) x⇒0+

A:

Q: Evaluate

A: To evaluate limx→0 e2x-1xSubstituting x=0 , 00 form is obtained Hence , L' Hospital's rule can be…

Q: iv. f(0) = Preview v. lim f(x) = x→7 Preview vi. lim f(x) x→7+ Preview

A:

Q: V-x – 2 – V3 te lim x--5 -x - 5

A:

Q: d. lim_f(x)= X4-2 e. lim f(x) = x--2 f. lim f(x) =

A: Since you have posted multipart question and we can answer three subparts. So, answered the first…

Q: b) lim x-13 X-0

A:

Q: lim (х — Vx? + х

A: Consider fx=x-x2+x. Simplify the above function. fx=x-x2+xx+x2+xx+x2+x=x2-x2-xx+x2+x=-xx+x2+x

Q: lim, 1 f(x) = %3D

A: limx→a f(x) =L if and only if limx→a- f(x) = L =limx→a+ f(x) .

Q: Vx+4-Vx2+x+4 7. lim x-0

A: Explanation and solutions is given below....

Q: lim x+0 v25 + 8x – 5

A:

Q: g(x) lim -2 h(x)

A: Please refer to the image below

Q: e7x + e-7x _ 2 lim x → 0 5 x2

A: Evaluate the given limit as follows. limx→0e7x+e-7x-25x2=e70+e-70-2502=1+1-20=00 Since 00 is an…

Q: lim (x²+2) sech(x) X → 00

A:

Q: Evaluate the limit.

A: Given:                     limx→∞e4x-1-4xx2 Dividing the numerator by highest power denominator:…

Q: 3. y = f(x) 4 6. -1 lim f(x) =

A:

Q: iv. f(0) = Preview v. lim f(x) = Preview %3D vi. lim f(x) エ→7* Preview %3D

A: f(x) =7x3+8xx2-7x(iv) f(0) = ?f(x) = x7x2+8x(x-7)=7x2+8x-7f(0) =0+80-7=-87⇒ f(0)=-87(v) limx→7- f(x)…

Q: (a) f"(2)> 0 (b) lim f(x)=5 x→ -00 f'(2) = 0 lim f(x)=5 f(2) =1 Pts of inflection at x = -2 & 2

A:

Q: Evaluate the following limits.

A: If any function is continuous within a given interval, then its limit must exist in that interval.…

Q: (b) lim (1+ x)* x→0+

A: Given

Q: lim (lnx/x1/2 - 1/x)  ? x-->infinity

A:

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: (g) lim (x- Vx +x - Vx-x (h) lim 3x²

A:

Q: lim h0 S(x + h) – f(x) + lim h0 g(x + h) – g(x) (S(x + h) + g(x + h)) – (f(x) + g(x)) , %3D lim ? h0

A: We have to check that whether,  limh→0fx+h-fxh+limh→0gx+h-gxh=limh→0fx+h+gx+h-fx+gxh is always true?

Q: Q2/Find the limiting values: tanC4x) lim 必→。 2 lim 7 ダー x そん

A:

Q: (d) lim f(x) = %3D x→-1 (e) lim f(x) = x→0 (f) lim f(x) = x→2+

A: Solution-

Q: (込) 6. (d) lim x→3x-3 x² -9

A: Find the limit . Of [1/(x-3) -6/(x2-9)] when x tends to 3

Q: xsinx lim x→0 e*+e¯x-2cosx

A: Since, we have been given up the expression:-limx→0 x sin (x)ex+e-x-2 cos (x)-(i)Since,on applying…

Q: d) (x+27) -3 X lim-

A:

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: Find the limits

A: To determine: limx→∞ x2+3+x

Q: (c) lim xe-x/2. x 00

A:

Q: e3x + 5e* (с) lim x→0 7e3x – Te™

A: We have to evaluate the given limit.

Q: lim (2a +x) X-

A: We find the limit by substitution

Q: c) lim x→b x-b Vr-5-5 5 – 5 d) lim x-+9 x - 81 e) sec mx – 1 lim

A:

Q: x² yey lim(x,y)→(0,0) x4 + x + y²

A: To evaluate the following limit.limx, y→0, 0 x2yeyx4+x+y4

Q: lim Q3/ Evaluate -costx) 3 sec x (1+ X /2

A:

Q: 2 V - 3 lim x – x→0 9 – 5 x 3

A:

Q: d. lim f(x) %D X-3-

A:

Q: h +2h (d) lim 3h -h' +5x+4 (e) lim x' +x-12 -3x +5x+4 lim 4x +x-12

A:

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

A: Topic = Limits