2.x2 – 3 x < -1 f(x) = 2.x3 +3 -1 < x < 1 2.x2 + 3 x >1 Enter DNE if the limit does not exist. a) lim f(x)= r--1- -) lim f(x) = 2+-1+ -) lim f(x)= =) f(-1) = e) lim f(x)= I+1- → lim f(x)=| g) lim f(x) = 2+1 n) f (1) =

Q: Find the limit of sin(6x) limy→0° sin(2x)

A:

Q: By considering different paths of approach, show that the limit xY COS Y lim does not exist.…

A:

Q: 18 To determine whether L'Hôpital's Rule applies to lim follow the same procedure as in step 1. X0…

A: To write that L-Hospital rule applies or not

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: (1) limx-ol-cos x 2 sin²x (2) limx-0 x-³…

A:

Q: estimate the limit numerically to two decimal places or state that the limit does not exist

A: Given: Plugging the limit directly, we get:

Q: 1) Show that the limit doesn't exists : ysinx 3) lim (x,y)→(0,0) x²+y2

A: To show that the limit of a multivariable function does not exist,…

Q: Find the limit: limit of 1-cos3x/cos5x-1 as x approaches 0

A: Given,

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol 1-cos x sin²x (2) lim, o…

A: 3 1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0 (tan-1x-x) x-3

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x→0 sin 2x

A: Here we will find out the required value.

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x sin²x (2) lim, o…

A:

Q: Find the limit. Enter DNE if the limit does not exist. 15zy lim (2,9) → (0,0) 22+ y?

A:

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) limx¬(n/2)-(tan x)cos x (2) limx-o…

A:

Q: 2. Find the the limit. li -y 1 (tany): 2 Y- 2

A: Given that:                limy→π2-(tan y)π2-y

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x

A:

Q: 1 if x – 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = x -…

A:

Q: b) Use L'Hopital's rule to find the limit: 1/In x (In xv lim

A:

Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: Given: limx→01-cos3xx2 we know that a3-b3=a-ba2+ab+b2

Q: 4 Find the limit: lim sin(x) (Enter undefined if the limit does not exist.)

A: The given limit limx→04x-4sin(x)

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: 18 To determine whether L'Hôpital's Rule applies to lim follow the same procedure as in step 1. X-0…

A: L hospitals rule can apply only if the direct substitution will yield an indeterminate form meaning…

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

A:

Q: 1 lim xcosx Xcos x

A:

Q: compute limit as x goes to 0 of (sin(x)-x)/(x^3)

A:

Q: In(1+ x?) lim x-0 x3

A:

Q: find the limit:  limx→∞ (ln x)^3 / x^2

A:

Q: Evaluate the limit: cos²(x) – cos(2x) lim

A: We have to find the limit

Q: 9 -x2 if x 1 .What value of c makes g(x) continuous at x = 1? Show all conclusions. 2 Vx-4 Using…

A: For a function to be continuos, the left hand limit should be equal to the right hand limit.…

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 (1) limx-o[: 1-cos x 2 sin²x (2)…

A: We have to find the limit using L Hospital rule.

Q: Find the limit analytically: 2-4x lim 40 5+3x 1. x - 2x-15 lim x 5 2. Find dy/dx of: x' (x- y) -x-y…

A: The given data is: The strength of the rectangular beam is proportional to the square of width and…

Q: 1- cos 2x 5. Calculate the limit lim using a) l'Hopital's rule b) vanishing functions x sin 3.x

A: For the solution follow the next steps.

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 2 (1) limx-o[: 1-cos x sin²x (2)…

A:

Q: How do you evaluate the limit:  limx--&gt;0 (1-cos(7t))/(sin(7t))   WITHOUT using L'Hospital's rule?

A: Since the given function is function of  variable t but in question limit is given for variable x.…

Q: . Suppose f(т/3) — 5, f (т/3) — —3,а sin(3та) 2->0 sin(5Tx) . Find the limit: lim

A:

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

A:

Q: Evaluate sin(x – 3) - lim x→3 x2 + 1x – 12 Limit = (Enter DNE if the limit doesn't exist)

A:

Q: Prove that lim x cos 4 = 0. X-0 -1 s cos(4/x)s 1 = -x s cos(4/x) s x*. since lim (-x*) = x-0 and lim…

A:

Q: In(x/4) z+4 x2 – 16 (Enter undefined if the limit does not exist.) Find the limit: lim

A: Solving the problem by finding the limit of the given expression.

Q: In(3x) EXAMPLE 3 Calculate lim SOLUTION Since In(3x) → o and → o as x - o, l'Hospital's Rule…

A: Given:         limx→∞ln3xx3 L'Hospital's Rule:         limx→cfxgx=limx→cf'(x)g'(x)  Since ln(3x)→∞…

Q: - Find the limits using L-Hopital's Rule: cos 3x 1 (а). im $ x→0 X* (b). lim (e - 1)*

A:

Q: x-3x+5 by X-0 4x2+2x+3 10. Find the limit: lim means of the L'Hopital Rule

A:

Q: 1f. Use L'Hopital's Rule to find the Limit: lim (tanx)x x-&gt;0+

A: Given,

Q: In(3x) EXAMPLE 3 Calculate lim x → 00 SOLUTION Since In (3x)→ ∞o and In (3x) 1/x lim x → 00 = lim…

A: Topic = Limits

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: 7. Show that the limit does not exist by approaching (0,0) lim .2 ,2 + y- (x, y) (0,0)

A:

Q: Evaluate the limit sin 7h lim %3D 7h Enter DNE if the limit does not exist. Limit =

A:

Q: (b) Use the sandwich theorem to show that limy0x°cos - = 0. 1 In order to apply the sandwich…

A:

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

A:

Q: 6 - x - x² if x ≤ 1 if x > 1 2x - 9 Calculate the following limits. Enter "DNE" if the limit does…

A: f(x)=  6-x-x2    if x≤1 2x-9         if  x&gt;1

Q: It f:[0,1]→R is a function that achieves a global minimum at 1, and we assume that limx+1- f(x) -…

A:

Q: -x e lim In(1+4e-x)

A: The answer is 1/4