Find the following limit. lim h 0 V2h + 1 +1 h→0 2.

Q: Vh+9-3 lim h h→0

A: limh→0h+9-3hSince given limit is 00 indeterminate form.Therefore, use LH rule and solve.

Q: Find the value of the limit lim tan 2 x (a) 1/3 (b) 2 (c) 1 (d) 4 (e) 3

A: To find:

Q: x³ + x²y+ 2y³ x² + y? ,3 lim (x,y)→(0;0)

A:

Q: Find the value of each of the following limits. If the limit does not exist, type DN (a) lim f(x) =…

A: Given,

Q: Use the e – 8 defintion of a limit to show that lim (6z – 4) = 2+ 6i z→1+i

A: The given problem is to show and evaluate the given complex limit by using the epsilon-delta…

Q: Calculate the following limit: lim (x,y) →(-1,1) 3y² + 3xy - x - y x³ + y³

A: Given, limx, y→-1, 13x2+3xy-x-yx3+y3

Q: 1 t 3 lim t3 t - 3

A: limt→31t-13t-3    = limt→33-t3tt-3   =  limt→33-t3t(t-3)

Q: evaluate the limit. lim e2 'i+ In(t + 1)j + 4k

A:

Q: Find the following limit. x2 + 16 lim (x, y) → (0, 18) arctan x² + (y – 18)2,

A:

Q: Evaluate the following limit using L'Hospital's Rule, when applicable: 2m2 [V16т + 4 + m→0 V9m +3…

A: Given query is to find the limit of the expression.

Q: Evaluate the following limit 5 - Va lim z+0 5 + Vx Answer:

A: We have to find the limit of limx→∞5-x5+x We know x is strictly increasing function in the interval…

Q: Find the limit (e ut+t g +tan(6t)k) lim -4to it- Sin2t)

A: We have to find the limit.

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

A:

Q: Calculate the following limits, if they exist. lim (7,y)→(0,0) 1 – cos(x² + y²) 1² + y²

A: Use the polar coordinate substitution

Q: Find the value of the following limits: 5y 1-limy→0 tan 10y

A:

Q: Find the limit. V17x + h – V17x lim h→0 h

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Find the limit as t-➜0 of r(t)=

A:

Q: Find the following limit if there exist: x²y lim r.y)-(0.0) x3 + 2y3 Please choose one: a.1/3 b.1/5…

A: To find lim(x, y) → 0, 0 x2yx3 + 2y3

Q: Find the limit: limt t→0⟨(e^5t)−1/t,t^11/(t^12−t^11),−7/8+t⟩ ⟨  ,  ,  ⟩

A:

Q: Find the limit of the following lim  etan(x) x→  (5pi/2)-

A:

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

A:

Q: Find (in terms of the constant a) V5(a + h) – V5a lim h-0 Limit = DNE

A: We have to find

Q: lim; 0 (, cos t, In t). t+1

A: limt→01t+1, cost, lnt

Q: Evaluate the limit: 1-Cos(9h) lim h h >0

A: Find the limit When we plug in 0 for h, the denominator becomes 0 So it is undefined.

Q: Evaluate the following limit using L'Hospital's Rule, when applicable: 2m2 [V16m + 4 + 9m + 3 lim…

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.). V1 + h 1 lim h → 0

A: Authoring guidelines:…

Q: lim (t – [t]) t→4+

A:

Q: Show whether or not the following limit exists: xy³ lim (x,y)→(0,0) [x2 + y6

A:

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: 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: Pls help ASAP

A:

Q: Choose the correct answer for the following limit Vasin t² dt 2 x4 lim (A) -1 (B) 3. 1. (C) 8. /3

A:

Q: Find a value of the constant k such that the limit exists.

A:

Q: Compute each of the following limits, or show that the limit does not exist. xY (b) lim (x,y)→(0,0)…

A:

Q: Given that f(x) = e ,which of the following is equal to the limit F(; + h) – f(}). lim h→0 ? h Oe…

A: From definition of derivative we know for a function f(x),  limh→0f(a+h)-f(a)h=f'(a)

Q: Find the following limit. x2 + 15 lim (х, у) — (0, 20) arctan + (y – 20)2,

A: We will find the limit as following.

Q: Evaluate the following limit, if it exists: lim (x,y)>(0,0) x² + xy+ y²

A: We have to evaluate the limit lim(x,y)→(0,0)x3-y3x2+xy+y2 if it exists.

Q: Find the limit, if it exists. lim x+ 00 ex O A. ex O B. - 0 O c. 0 O D. o

A:

Q: e find if the limit exist lim てX,ソ)→ (o0) x² yz

A: Given function is: fx,y=x2y2x4+3y4 We have to find the limit of the function fx,y as x,y→0,0.

Q: Find the following limit: lim f(x) O A. 0 О В. О Ос. 3 O D. 4

A: We have to check

Q: Evaluate the following limits, where c and k are constants.

A: See the details solution in below

Q: Find the limit by numerically. 1 lim 1 + |t| |t – 1| t-0

A: To find the limit numerically, consider approximately some values of t which are closer to 0 from…

Q: Please

A: Given limit is By L'Hopitals' Rule, we have

Q: lim (x,y)→(0,0) 2.x²y + 5xy? x3 + y3

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)  lim t→0  (1/t) -…

A: Given limt→01t-1t2+t        ⇒limt→01t-1tt+1∵taking 't' common         ⇒limt→0t+1-1tt+1∵ using…

Q: What is the the value of the limit lim,o Vn (Vn +1– yn)?

A: Limit of the sequence

Q: Evaluate the limit using the Limit Laws: lim t→7 t^−1=

A: To evaluate the limit, limt→7 t-1

Q: Vx+x? a) lim x+00 5x-x2

A:

Q: Find the following limit and show that either the limit exists or not lim (x,y)¬(0,0) xy sin 2 + y²)…

A: claim - to show either the limit exist or not  limx,y→0,0xysin1x2+y2 as we know, limit exist if…