x(T/2)+ x 39. lim x csc x X21T x22x 1:

Q: e* – 1 lim V1+x -1 x→0

A:

Q: (х-а) 2. lim Vx-Va X→a

A:

Q: 8. (x - 1) dx √x lim

A:

Q: X x+cos (-3x) 16) lim

A: To find the limit  limx→-∞xcos-3x

Q: 2) lim (x – T)tan5

A:

Q: x' - 4x? – 9x+36 lim b) x - x-12 x-3 e* -e* – 2x lim c) x- sin x

A: limx→-3x3-4x2-9x+36x2-x-12=limx→-3x2x-4-9x-4x2-4x+3x-12=limx→-3x2-9x-4xx-4+3x-4=limx→-3x2-32x-4x-4x+…

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: for e5x – x³ x 0 (i) lim h(x) (ii) lim h(x) (iii) x→0- x→0+ lim h(x)

A:

Q: 2x -cos(2x)- 2x - (b) lim | x2

A:

Q: 2x2 – x – 3 (d) lim x→-1 x² + 5x + 4 2x – 8 (e) lim r→4 x2 – 8x + 16 x2 (f) lim r--2 2x + 4

A:

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

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

Q: f (x+h)- f(x) 7x3-2x-1 Using lim-0 Find the slope of the tangent line y 5x+2 h at x = -1.

A:

Q: Vx +1- 2 (c) lim x→3 X – 3 2e-* +3 (d) lim 3e* +2 00-X

A: Topic:- application of derivatives and calculus

Q: x t 4x +3 x- x -2 f(x): 1 [x +3] 17X71- x 2 1 lim f(x) f(x) lim x-> 2

A:

Q: (t³ + 8)-dt + 8)-šdt lim

A:

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: lim (- %3D x2 - 2sinx + 2x O 1 42

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: Vx+2-3 (a) lim x→7 х—7 4x +3x – 10 | (b) lim х> -2 х* +8х +12 sin xcos x (c) lim x→ 0 x(х + 6)

A:

Q: t(x)=6x/ ln x 10 What is lim               x →+∞ t(x)?

A: It is given that, the function

Q: Vx+1- /2x x² - x 2х f ) lim x→1

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: Зx +3x+5 х +2 1-cos.x (а). lim (b). lim

A: To evaluate the limit, limx→∞3x3+3x+5x3+2, plugin the limit and obtain the indeterminate form of the…

Q: Find the limits in Exercise

A: limx22-1x

Q: (b) lim (1+ x)* x→0+

A: Given

Q: (-x² – 6x–10 xs-2 1. lim g(x), where g(x)={ x>-2

A:

Q: (1 – V3x lim tan- 3 + x x-00

A:

Q: 4x e lim x→0 r2

A: The series expansion of ex is ex=1+x1!+x22!+x33!+x44!+...

Q: 1 1 V13+x 3 h. lim X→0 X + 4

A:

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

A:

Q: 2. メー gu)= - fex) = X üls Is1 3メ-1 احب lim (fog) x メー

A: We have to find limit

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

A: here is the solution

Q: |x² +1 if x 0 x→0

A:

Q: Find the limit.

A: We have to find the given limit

Q: x2 – x – 12 lim 2. Evaluat" t→4 3x – V16 – x

A: Limit is the value of the expression as the independent variable approaches certain value, not…

Q: -Sx-2x+4 d. lim x-9x+1 e. lim xo 3x2-2x-15 x249 f. lim 0 2x+2x2-3

A: Limit   If a constant number is decided by infinity then it will tend to zero .

Q: x3 – 11x lim x→0 x V5x+11

A: Consider the limit limx→0x3−11xx5x+11

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: 1. lim f(x) where flx) = (-3x + 8 if x -2

A: Use limit condition.

Q: x2 – 4 lim h→2 Vx – V2 /9 + h – 9 - lim h→0 h

A:

Q: x + 3x – 1 lim V4r6 – 2x エ→ーx 2.r

A: We have to find limit

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

A:

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

A:

Q: 2xy lim (x.y)-(0,0) x² + 2y6

A:

Q: 4x° – x lim x' +5 (d) x² – 49 lim Vx+2 - 3 (e)

A:

Q: х — 1 lim x→1+ Vx + 2

A: Here we need to find the right hand limit only.To find the required limit substitute the variable…

Q: Find lim (x2 + y?)ln(x² + y?) (x,y)-(0,0)

A: To findlim(x,y)→(0,0)(x2+y2)ln(x2+y2)