30. Suppose that f, f', and f" are positive on R. Prove that lim f(x) = 00.

Q: Suppose that f(x, 0) = 3 for all x ≠ 0 and f(0, y) = 5 for all y ≠ 0. What can you conclude about…

A: The limit of the function, f(x,y) at a point (a,b) does not exist if two paths upon which the…

Q: Find the limit, if it exists.

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

Q: 5. If b > 0, prove that lim = 0. %3D 1+nb

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

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: Determine the following limits analytically.

A:

Q: In (x +h) – In (x) is When x = 2e, lim h→0 h

A: Substitute x=  2e above

Q: 4) Find the following limit or show that it does not exist. sin(ry) a) lim (1,y) (0,2) b) lim…

A:

Q: Compute the indicated limits. 2x + 5 lim cos 3x? + 2x – 5

A:

Q: Prove rigorously that lim lxl = 0.x→ 0

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: Evaluate the limit: sin(5x) cos(6x). lim x→0

A:

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

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

Q: Find the limit, if it exists

A:

Q: Prove that lim(x,y)→(1,2) (x2 + 2y) = 5 by using the precise definition

A: ε-δ definition: Limit of function f(x,y) at a point (a,b) is 'L' if for every ε>0 there exist…

Q: Compute limit as x goes to infinity of (cos(x))/(x)

A: We find: limx→∞cosxx We solve this limit by using Squeeze theorem. Squeeze theorem states that if…

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: Find the required limit or indicate that it does not exist. lim o+ (in (t6), 12 in t O 6i O Does not…

A: We have to find out

Q: Suppose that f is decreasing on [a,b]. Prove that that b. lim Rpf) exists and equals to Ilp||+0

A:

Q: We want to find the limit lim os(2æ) – cos(7x) - x2

A:

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: Compute the limit as x goes to 0 of [tan(x) - sin(3x)] / (x^2)

A: limx→0[tan(x)-sin(3x)]x2=[tan(0)-sin(3(0))]02=00

Q: Evaluate the limit. lim     In (Sinh x)x →0+

A: we have to evaluate the limit. lim     In (Sinh x)x →0+

Q: 5. Use the definition of limit to prove that lim[(x – 1)(sin x²)] = 0

A:

Q: 1-cos 2x lim 4x

A:

Q: 2. Compute xe" da using a limit.

A: The given which we have to find the integration from 0 to ♾️  f(x) = xex

Q: Verify numerically that:

A: To verify: limh→0eh-1h=1

Q: 1. Prove rigorously that the following limit does not exist lim arctan x-0

A: limx→af(x)≠L: There exists ε>0 such that for every δ>0, there exists x such that…

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

A:

Q: 2. Let r > 1. Prove that lim r" = 00,

A:

Q: 1. Prove that lim vx sin O using the Squeeze Theorem.

A: Using squeeze theorem,

Q: Use Squeeze Theorem to evaluate -2x lim e COS x x 00

A: Based on the squeeze theorem or it is also been called sandwich theorem we can evaluate the limit by…

Q: 2

A: According to the given information, it is required to prove the limit using epsilon delta…

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

A:

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

A: We have to find the limit

Q: エ→2ー Prove that lim sin(1/x) does not exist. Lot II

A:

Q: lim cos x*/x x→0

A: Given,          limx→0cosx1x

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: cos x – 1 + x² lim x4

A: Given: limx→0cos(x)-1+12x2x4

Q: If 2 - x2 <=g(x)<= 2 cos x for all x, find lim x-->0 g(x).

A:

Q: Find the limit: 1 – cos(x) lim x2

A:

Q: Find the limits limx→e+(ln x)1/(x-e)

A: Limit:      x→e+limln x(x-e)=h→0limln (e+h)(e+h-e)

Q: 12 Show that the following limits do not exist. 1 lim X0x (a) (x > 0), 4,

A:

Q: evaluate the limit.

A: We want to evaluate the following limit.

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: 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: Compute the lim as x goes to 0+ (e^x - 1 - x)/ (xe^x - x)

A: we have to compute the limx→0+ex-1-xxex-x

Q: Find the limit. lim Cn (3+x)- In (l+x)]

A: