3. Evaluate (3x² + 1)dx by using the limit definition with the right end points. (Don't use the Fundamental Theorem of Calculus. Use lim R = lim )f(x,)Ax) %3D Tn 00 n 00 j=1

Q: 4 Find the limit: lim t+0 t 4 et – 1, (Enter undefined if the limit does not exist.)

A:

Q: 2. Compute the following limits at infinity and give reasons for your answers. 1 a) lim b) lim I00…

A:

Q: Jse the two-path test to prove that the following limit does not exist. y* - 2x? lim 4 (x.y)-(0,0)…

A: Since tha value of both the limit is different  Hence the limit does not exist.

Q: 3. Use the epsilon - delta definition to prove that the limit is lim Vx x-0 371 when

A: To use epsilon delta definition to show that the below limit is 0. limx→0x3=0

Q: 7 sin(T2) In (zº) q(z) = %3D What is lim q(x)? ncwor bolow:

A:

Q: 1: Find the limit 6x°y5 lim (x,y)¬(0,0) x6 +y10

A: See the attachment

Q: Evaluate the following limits (if exist): 1-cos(ax) (c) lim- a+0 (d) lim/Vxr'+x-Vx°-cx), where c is…

A: To evaluate the given limit we are using L- Hospital rule

Q: 2. Use L'Hospital's rule to evaluate the following limit. cosh(3x) – 1 lim x→0 x2

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: Express the limit as a definite in 7 lim 1 + (i/n)3 n→ 0 n i = 1 1 7n dx 8

A:

Q: (a) Determine the following limits without using L'Hôpital's rule. V7x° +4x -x² -2 lim x'-2x-3x+1…

A:

Q: What is the limit of f(x) = 3 as x approaches π? (If an answer does not exist, enter DNE.)

A: Given:

Q: (d) Determine the following limit using u-substitution method: sin(t - 1) lim -1t2 +t – 2

A:

Q: 2. Use the paths x = y and x = 0 to verify the limit. lim (x.y)-(0,0) x2+y²,

A:

Q: Recall that J x+ 4 |x +4| = ((x+4) X <-4. Therefore, we will need to check the limits when…

A: NOTE: Refresh your page if you can't see any equations. . as we know,

Q: To apply the divergence test for ,3/n² n=1 we need to evaluate lim e3ln? n→∞ What is the value of…

A:

Q: Use the E-8 definition of a limit to prove lim Xy (Xy) →(0,0) x² +y²

A: Consider the equation

Q: Find the value of the following limits: 5y 1-limy→o tan 10y 2-limx-0 6x cot3x 7x²+8x 3-limx-0 4x²…

A:

Q: Use l'Hôpital's Rule to find the limit. 5t +t 5t t-0 e lim 4 -t

A:

Q: 1 is equal to cOs x - The value of the limit lim x2

A:

Q: 4. Evaluate the limit of as e approaches 0. 2a A 2 B. % CO D. infinity

A:

Q: Use a table of values to estimate tne value of the limit of lim Vx + 4 – 2 f(x) f(x) 2.

A: Consider: limx→0x+4-2x   Let fx=x+4-2x Since we have to calculate limit at 0 of fx=x+4-2x.  Make the…

Q: 2 Show that the following limit does not exist. lim Ty Cos y (r.9)-(0.0) 3r+ y²

A:

Q: Use the Squeeze Theorem to prove lim = 0. x00 x+ e- For x 0, since 0 < e* <1, we have

A:

Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

Q: Determine the 2.x2 – 4x + 6 dx using the definition. (hint: lim Rn)

A: Given: ∫12 2x2-4x+6 dx  To find: Value of the limit.

Q: Compute the limit as xà0 of f(x)=(sin(61x))/x, if possible.

A: To find:limx→ 0sin61xx

Q: Compute the following limit, or verify that it does not exist: xY lim (x,y)→(0,0) 2x² + 3y2

A: Given that limx,y→0,0xy2x2+3y2 fx,y=xy2x2+3y2 (i) Put x=0 and then y=0 in fx,y find the value of f1…

Q: Find the value of the.limit Olim Jx+z - V3 X+2 @lim Vx+6 x3-2 X+2

A: A number M is said to be the limit of a function f(x) at x=a if for any arbitrary chosen positive…

Q: 2. Use the definition of the limit to prove that lim (r+2y – 1) = 1. (1,9)¬(0,1)

A:

Q: 4 Find lim cos C→十0 Enter I for o, -I for –∞, and DNE if the limit does not exist. Answer:

A: Topic = Limits

Q: Show the limit lim (x,y)→(0,0) x4 + y² does not exist.

A:

Q: Show that the limit does not exist. xy? - 1 lim (Ky)→(1,1) y-1

A:

Q: Estimate the limit numerically. x² lim x+4 O diverges to +o 00 O diverges to -∞

A: Given

Q: 6ln (1+x) lim х>0 2е3х—2secx

A:

Q: In(t³ + 1) + t³ + 1 r(t) = 4: then the limit lim r(t) equals 1-0 -i-(4e-²¹-5e²¹)j- - sin³t -k, 13

A:

Q: 11. Show that the limit lim (z.y)→(0,0) r² + y4 does not exists.

A:

Q: 1) Show that the limit doesn't exists : 3x2 Jy 2). lim (x,y)→(0,0) x2 +y²

A: We have considered different paths y = mx. If the limit is independent of m then the limit shall…

Q: 1 lim x sin x x2 x→0 O 1/5 O 1/7 О 16

A: Given, limx→01x sinx-1x2

Q: S 10 – x – a? if x 1 Calculate the following limits. Enter "DNE" if the limit does not exist. 2x +…

A: The given function is f(x)=10-x-x2if x≤12x+6if x&gt;1 We have to calculate,  a) limx→1-f(x)=?b)…

Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→ ∞ x²

A:

Q: 1. Show that the limit does not exist. xy? lim (x,y)→(0,0) x² + y4

A: This question is related to limit in two variables.

Q: 3. Compute the limit algebraically Vx +3x2 lim 6x 1

A:

Q: 2. Calculate the following limits. sin 3x a) lim х-0 2х(х-3) V4+h-2 b) lim h→0 h 5х-4 c) lim X→∞…

A:

Q: Evaluate the limit sin 2x lim z+0 9x

A: Answer and explanation is given below

Q: 2. Find the limit using Squeeze theorem 1 lim,2|a – 2| sin( `x – 2

A: Given: limx→2x-2sin1x-2

Q: 3. Compute the limit algebraically Vx + 3x2 lim 6x 1

A: Solution: The objective is to find the limit of the given function

Q: By using the de finitionof the limit, prove thal (D Lim x (x+1)=D0 e) Linx cos= o

A: Let f(x) be a function defined in the open interval a,b and let c be a point in the interval a,b…

Q: S, f(x) dr may not equal lim , f(x) dx. Show that 2x dx x* + 1 diverges and hence that 2x dx ? + 1…

A:

Q: 5x2 + 10х + 1 :0. lim x4 + x? + 1

A: