lim x→pi/10  tan(48*x) lim x→0+  sqrtx*e^sin(pi/x) limx→0  x^2*sin3/2x

Q: lim x approaches 0 .............. (sinx)^2

A: Given:              limx→0 sin x2 Plug in the value: x = 0             =sin02

Q: solve using L'Hopitals Rule 6. Lim    (2tanx - sin2x) / x3   x->0

A: limx→02tanx-sin2xx3

Q: If tanx=sinha prove that a=ln(secx+tanx

A:

Q: solve using L'Hopital's Rule 1. lim      [ 1/(sin^2 x) ]  - [ sinx/x^2 ]    x->0

A:

Q: sin 5x 1. limx-0 2x2 +3x 2. limx→0 x3+x+1

A: 1).limx→0 sin 5xx2).limx→∞ 2x2 +3xx3 +x+1

Q: sin(Tæ) lim x → 12 In(x – 11) -

A: The given limit,          limx→12sinπxlnx-11

Q: lim x-->0 (1+sinx)^(1/x)

A:

Q: limx→0  (x^2+3) / (1−cosx)

A: given example is, limx→0x2+31-cosx

Q: 2 xt (* sin) lim sec x lim X→+0 X. 2

A: Given limits are  1) limx→∞xsin2x2)limx→π2secx3)limx→0sinxx

Q: sin(2x) limy→ 0+ X

A: Given:     limx→0+sin2x2

Q: ON 3 sec3(In x) + sec2(In x) tan(In x) 2х n x) tan(In x) n x) dx c³(In x) + sec²(In x)

A: We have to choose the correct option according to the given information

Q: lim x----->0    sin x sin 2x/1- cos x

A: Given:-  limx→0  sinx  sin2x1-cosxTo find:-     value  of the above limit.Concept:-  Use 'L Hospital…

Q: Find the value of* cos(x) sin (2x) lim sin(x) – 1 - O 0/0 4. O (intinity)

A:

Q: x' sin (tanx*) -1 Integrate 1+x

A: Introduction :

Q: limx>0 sin-1x/x

A: So, now we apply L' hospital rule to evaluate the given function. Because if we directly apply the…

Q: lim (sin x)tanx TT 2

A: We will solve the problem

Q: sin x-coS X Determine el límite: lim 1-cotx

A: The given expression is limx→π4sinx-cosx1-cotx. Evaluate the limit as shown below.

Q: limx>0 (x-sin(x))/xsin(x)

A: Given,          limx→0x-sinxxsinx

Q: limit of x approaching 0 from the right of ((sin(x^2))^x )

A: Given   apply squeeze theorem

Q: sin 2x ind lim X-0

A: Given that: 1. limx→0sin-12xx2. ∫x(x-2+x3)dx

Q: Find the limit

A:

Q: Limit as x approaches 0 of Sin(5x)/(2x

A: Limit as x approaches 0 of Sin(5x)/(2x

Q: 4x+sin x lim x→02x - sin 3x

A: We have to solve given problem:

Q: しx)f erentiate f メて ×ケ-X arcsin (3x -1)+ In (5x*+3) 6arctan (1-x) . メ9 fon

A: f(x) = sin-1(3x-1) + ln(5x4+3)

Q: (sinx -) (3sin²x -sinx +1) lim TE +X, 2

A:

Q: x+1 1-x In [cosh (x+1) + sinh (x+1) lim 2tanh x=1- lim_ In x=1+ l

A:

Q: (7x – 10,* lim x+0 7x lim 2x sin- 9 sin 27x lim x2 21x lim x+00 12 – 3x

A:

Q: 2. lim x sin(1/x) X18 ex+2x 3. lim X18 ex

A:

Q: lim x -> pi/4 sinx-cosx/1-tanx

A:

Q: solve using L'Hopital's Rule 2. Lim      (x-sinx) / (x^3)    x->0

A: To find: The limit of limx→0x-sin xx3. Calculation: Apply L'Hospital rule: limx→0x-sin…

Q: Arcsinx-sinx 1. lim x→0 (1-cos2x)sin2x 2-2cosx-xln(1+x) 2. lim x→0 x sin² x

A: 1)

Q: solve using L'Hopital's Rule 7. Lim    1/(tan-1)2  -  1/x2    x->0

A: Given the limit as : limx→0 1tan-12-1x2 We need to find the limit by using L' Hopital's Rule. Let's…

Q: lim x→0 (sin3x sin5x/x2) *without use of deritivatives or l'hospital's rule*

A: See the details solution in below

Q: 2 sin(x)-sin(2x) х-sin(x) lim X→0

A: Given,           limx→02sinx-sin2xx-sinx

Q: sin 2x + 2 arctan (k) lim x→0 In (1+ 3x + sin 2

A: Introduction: So, according to L'Hospital's Rule, if we have an indeterminate form 00 or ∞∞, all we…

Q: Integral of Sin^5 x dx

A: We need to find We know that

Q: 4. lim (sinx)tanx X0+

A:

Q: 2 sin x lim In

A:

Q: 1 lim x-0 (sinx ズ→ X.

A: Evaluate the limit limx→01sin x-1x. Rewrite the expression: limx→01sin x-1x=limx→0x-sin xx sin x…

Q: Integral of sin^4 (x/2) cos^2 (x/2 dx

A:

Q: 1- Sinx+ Sin'x 4 X. 2 1-Cosx+Costx 1- Sin'x (1- Sin²x) (x, 1-Cos'x (1-Cosx)

A:

Q: limx→0 sin 2x 2x²+x

A:

Q: sin 2x – x lim x→0 3x

A: Given,limx→ 0sin2x-x3x

Q: x+13 dx х+4

A: 1) Evaluate: ∫3x2+14x+13x+4dx

Q: sinh (2.Inx) n(coshx+Sinhx)+in(cashx-sinh x).

A: We have to rewrite the given expression by using the exponents.

Q: sin 2x (c) Determine whether the improper integral dr converges or diverges. If V1- cos 2.x it…

A:

Q: imit x to infinity sin3x/2x

A:

Q: (1) limx→(π/2)-(tan x) (2) limx→0 x ³(tan-¹ x - x)

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