Evaluate lim,→0 ela-cos 7x 8 sin x 7

Q: Evaluate using a substitution θ =11x

A: Given limit  limx→0 sin 11xx Since we have an indeterminate form of type 00. Apply the L' Hospital's…

Q: (d) Evaluate: 1-cosx lim tan2

A: To evaluate: limx→01-cos3xtan2x which is a 00 form. Therefore, to solve it, we need to apply…

Q: Evaluate tan 3x2 + sin² 5x lim

A: Here we have to evaluate       limx-->0[tan 3x2 + sin2 5x]/x2

Q: Evaluate using substitution. lim 3 sin x x→ -π/2

A:

Q: 1 Evaluate the lim sin x>0

A:

Q: Evaluate each limit. sin x + 6 sin x + 5 lim xS3p>2 sin x - 1

A:

Q: tan 5x lim x-

A: Consider the following limit: limx→0tan5xx Apply L'hopital rule to the above limit:…

Q: -1 sin (5x) lim

A: The given expression is limx→0sin-15xx the given expression is the indeterminate form 00 Apply L'…

Q: æ In(sec(2æ)) (sin(3x))³ lim x→0

A: Given,             limx→0xlnsec2xsin3x3

Q: Find the value of Tx³ + 2. lim [sin x3 + 1 -1 1 O O

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

Q: (:) -*) Evaluate: lim 1 ба" sin 6.

A: Topic-limit calculation

Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

A:

Q: Evaluate: lim, (cos z). Show your solution. O -1

A: Limit of a function f(x) at point x = a exists only when Left hand Limit(LHL) = Right hand limit…

Q: If a > 0, show that sin(nx) lim d.x 0. n→∞ nx

A: Solution

Q: find the limit or explain why it does not exist

A: limx→0cos2x-1sinx

Q: Exaluate the following limi- 1. lim to + x' xー>-○ x(- 2x2 +5) x° 2. lim sin 3(2x+1) ×ー>-ム 2 2x +1

A:

Q: 2. tanx カイ Lim (3, 주 so +1 wi7

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

Q: Q\ Find lim tan(x)cos(x) O 2 -1

A: The given limit is of the form ∞0 form. Let L=limx→π2-tan xcos x⇒ln L=ln limx→π2-tan xcos x…

Q: Evaluate using substitution.

A:

Q: lim = 0 sin x.

A: limx→01x-1sinx=0

Q: Q:B/ Find lim, [tan x-sec x].

A:

Q: (a) Show that tan x = sec?x using quotient rule. dx x+8 (b) Find lim X-2 x+2

A: Solution-

Q: Find values of a and b such that sin 3x + ax + bx³ lim = 0 x3

A:

Q: Evaluate: lim   (1−cos−1x)csch(1−x) x→1−

A: We have to find the limit.

Q: Find the lim using l'Hospitals Rule tan (7x). Sin ( 8x) lim X>0

A:

Q: Evaluate using substitution. lim tan -1 (ex)x→ 0

A: to evaluate the limit

Q: sin x 34. lim 1 - x o0-r

A:

Q: Clearly explain why lim (sin-(t) is equal to 1 and not zero. t+0+

A:

Q: Find the limits

A: We first try to find the limit by substitution

Q: Evaluate: lim (cos x)=¹2 X x → 0

A: Since the numerator is positive and the denominator x^2 approaches zero and is greater than zero for…

Q: Show that lim |x|cos 0.

A: We have to prove that limx→0xcos1x4=0. Use property, if limx→a−fx=limx→a+fx=L then limx→afx=L. First…

Q: 1 lim x COS X

A: See this solution in below

Q: Use Squeeze Theorem to evaluate lim x → to COS X loga x

A: To use squeeze theorem to evaluate the below limit. limx→∞cosxlogx2

Q: Compute the indicated limits. sin(2x) lim 3x

A:

Q: Find x² lim x0 1 - cos x

A: Solved below...

Q: 30. Use the fact that lim x→0 sin x X = 1 (shown in video) to show lim x-0 1 - cos x X = 0

A: we will find the required.

Q: . Evaluate the following limits. 1.lim cos .2 () 2. lim sin x→0 (- 3. lim 3¬× X→-2

A: 1. limx→πcosx22. limx→0sinxx3. limx→-23-x

Q: tan(31x) lim x → 0 5x

A:

Q: Find the one-sided limit (if it exists).

A:

Q: 2. Evaluate cosxsin2x lim 1 – sinx

A: We need to find limx→π2cos x sin 2x1-sin x Now, put the limit in the function, that is put x=π2 .…

Q: ?? 13 Find lim (1-tan X/2) Secx

A:

Q: Find lim sin (4 T x). I -3

A:

Q: Evaluate: lim sin(2x) A) 2

A: Given that: limx→5π6sin(2x)

Q: tan 2x 27. lim x→0

A: Find the following limit

Q: Evaluate lim sin(x)(x +2) 4 8 3x/2+8/2 8 O Does not exist

A:

Q: Find Lim o'sin to Sin 02

A: We use the properties of limit and L'Hopital's Rule to find the limit in the given question.

Q: Evaluate each limit. 1 - cos“ x lim sin x

A: Given that : The limit is limx→0+  1 - cos2xsin x .

Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx

Q: Evaluate

A: Our Aim is to evaluate the limit given below:-limx→0tan (2x)x-(i)

Q: evaluate the limit.

A: Given limit is Since Therefore, by applying L'Hopitals' Rule, we have