59. Show that 0°0 is not an indeterminate form by showing that if f is a positive function and lim f(x) = 0 and lim g(x) = 00, then lim (f(x))8(x) = 0.

Q: Find the limit, if it exists.

A: Here given as

Q: evaluate using Theorem 2 as necessary.

A:

Q: (z+2 z< 0 sin (x) 0<æ Let F (x) = Then lim F (x) =

A:

Q: Find the limit. 15) lim V3 + cos2 x A) 2 16) lim (3 sin x - 1)

A:

Q: Find the limit. cos(x) – 1 +x2 lim x-0 2x4

A: It is given that, limx→0cosx-1+12x22x4.

Q: Use l’Hôpital’s rule to find the limits

A: The L’Hospitals rule is used to obtain limits of a function when it occurs in the indeterminate form…

Q: x cos(2x) (c) lim x-0 sin(-3x)

A:

Q: Use l'Hôpital's Rule to evaluate the limit. cos (3x)-1 lim x² 2.

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: Identify ALL the Indeterminate forms involved and determine the limit of: lim, 0+ (cos(x))*

A: We know that               cosπ2-x≤1=cosπ2-xx≤1x So, bt squeeze theorem,               limx→…

Q: Prove that lim |x|sin(1/x) = 0.

A: We need to prove that limit of given function is zero.

Q: Use L'Hôpital's Rule to find the limit. 5. lim x0 e2- xr- 1 5 cos x

A: l'Hosptital's rule provides technique to evaluate the limit with indeterminate form.

Q: Use l’Hôpital’s Rule to find the limits

A: Given: limx→π2-sec7xcos3x we know that  secθ=1cosθ so, limx→π2-cos3xcos7x  00 form it is 00 form, so…

Q: Find the limits in Exercise

A: Given,

Q: (c) Prove the value of lim Sin 3a o Cos 4Do NOT use L'Hospital's Rule.

A: The given limit is,

Q: Find the limits lim x→ -1+ cos-1x

A: We find the limit by substitution

Q: sin²t lim t3 t→0

A:

Q: Use l'Hôpital's Rule to evaluate the limit. 2 - 4x+2 lim 2. X>co X+5x+11

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: Evaluate the limit (1 – cos x)² sin² . lim x2(1 – e)4 COS X - -

A: Given limit is : limx→01-cosx2sin2xx21-ex4  To find the value of the limit.

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

A:

Q: Find the limits in Exercise

A: Given: limθ→π4tanθ-1θ-π4

Q: 1. Find the limit (if it exists). (If an answer does not exist, enter DNE.) 2 - x im x² – 4 sin 2x…

A: Find the limit of the given function  1) (2-x)/(x2-4) , when x tends to 2 .  2) sin(2x)/sin(3x) ,…

Q: Use l’Hôpital’s rule to find the limits

A: Given: limθ→π22θ-πcos2π-θ for evaluating given limit, we substitute θ=π2+h so,…

Q: Evaluate the limit.

A: We have to evaluate the limit: limh→0sin 9hh We know that limx→0sin xx=1 So making same angle of…

Q: [4] (a) Show that lim (xa)-(0,0) 2x+y? y-mx, or along any parabola y= exists and it's approaches to…

A:

Q: 6. Figure out the following limits without applying L'Hopital Rule. sin(r- 4) V2r -1-1 b. lim (2²…

A:

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim X0 sin 2x x2-16 2. lim X+4 (VI+5)-3

A: *to find :- limits, using L-Hopital rule.

Q: If lim f"(x) = +0o, then the trapezoid estimation Tn - | f(x) dx %3D x0* can never be within 10¯³ of…

A: Given that limx→0+f''(x)=+∞ And Tn≈∫01f(x)dx Error for trapezoidal method contains double…

Q: b) sin (2x) tan (5x) Find lim- (Can't use L'Hospital's Rule)

A:

Q: Compute the following limits if they exist. 2 - VE (a) lim 244 3 - V2x + 1 (b) lim r sin

A:

Q: )Use the Sandwich Theorem to show that lim cos x-1 =0. x2 Find f'(x) for f(x) = sec(vx2 + 1).

A:

Q: Suppose the functions ƒ(x) and g(x) are defined for all x and thatlimx→0 ƒ(x) = 1/2 and limx→0 g(x)…

A: Given limx→0fx=12 and limx→0gx=2we have to findfx.cosxx-1

Q: Prove rigorously that lim sin 1/x does not exist.                                    x → 0

A: Let the given limit be y - y = limx→0 sin1xy = limx→0 sin1x1x×1xy = limx→0 sin1x1x×limx→0 1xy =…

Q: Find lim 2x sin using the Squeeze theorem. x-0

A:

Q: x sinh x 1. lim x0 cos 3x -1

A: The solution of the problem is given in the next step.

Q: Find the tangent equation for the function: f(x) = Vx2 +5 at x=2? Find the limits by using L.Hopital…

A:

Q: 70. J, f(x) dx may not equal lim , f(x) dx Show that 2x dx o x² + 1 diverges and hence that 2x dx x²…

A:

Q: 2 cos(4x) – 4x² – 2 4. lim х-о sin(2x) —х2 — 2х

A:

Q: If 2 - x2 &lt;=g(x)&lt;= 2 cos x for all x, find lim x--&gt;0 g(x).

A:

Q: Find lim,0 sin (-:). 6 Enter I for o, -I for -o, and DNE if the limit does not exist.

A:

Q: Find the limit: 1 – cos(x) lim x2

A:

Q: Evaluate using Theorem 2 as necessary.

A:

Q: 20. Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A:

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim 0 sin 2 -16 2. lim 4 (V+5)-3

A: 1. Here limx→07xsin 2x is of 00 form, so by applying L. hospital rule, we get limx→07xsin 2x =…

Q: Q.3/ Find the limits for the following: 1) lim sin 7x 2) lim x0 sin 5x 3) lim V-3 x→9 ズ-9 x1x3-

A: We will find the limit.

Q: Which of the following limits does not yield an indeterminate form? a.limx→0 3x^2/x−sinx b.limx→2…

A: (a)lim(x→0) (3x2)(x-sin⁡x)=00form(indeterminant form)(b)lim(x→2) lnx2(x2-5x+6)=00form…

Q: Find the limit sin(3x)cos(4x) lim→0 x+xcos(5x)

A:

Q: Calculate the limiting value for 1 cos(x*) – 1+5x³ lim x→0 х16

A:

Q: Find the limit. tan(12t) lim t-0 sin(4t)

A:

Q: Compute the following limits if they exist. sec r - 1 (a) lim I0- r3 x – sin x (b) lim I0 x - tanr 2…

A: We are entitled to solve 3 subparts of first question so, I am providing you the solution of the…