In(x - 1)2 | 26. lim x→2 In(3 In(x - 1)

Q: Prove that lim 12 √16x +9y¹2 2 6 4x² +3y does not exist by showing that the limits along different…

A: We have to prove that  limx, y→0, 0 16x4+9y124x2+3y6 does not exist.

Q: Find the limits x2/3 + x1 lim X00 x2/3 + cos?x

A: Given: The function is f(x)=x2/3+x-1x2/3+cos2x   To determine: limx→∞ x2/3+x-1x2/3+cos2x

Q: Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the…

A: Given

Q: Find the limit. Vn2 lim + 8h + 19 - 19 h→0*

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Q: If f(x, y) approaches 1 as (x, y) approaches (0, 0) along the path y = mx, where m is any real…

A: To check whether the given statement is true or false.

Q: x²– y? lim (x, y)→(0, 0) x² + y?

A:

Q: lim 4 sin(x + n) + 3

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Q: Express the limit as a definite integral. lim 40 E xk A xk; [-5, 1] k=1 1 9x8 dx -5 x9 dx x9 dx x dx

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Q: Find the limits limx→q(ln x)1/x

A: Given,     limx→qln x1x

Q: Let lim,-0+ f(x) = -2, where 8r - 3 for r <0 f(x): | 4x – 2 for r2 0 f(r) = Then what is (the…

A:

Q: Compute the limit 1 a2 1 - x2 lim xa x а - What can you say about the derivative of f(x) = ?

A: Given limit :

Q: Find the limit of the transcendental function. lim x → T/2 4 sin x

A: Definition of limits helps to find the limit of the given function. The value is said to be the…

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&gt;0 there exist…

Q: What is the limit of f (x) = 1 as x → T?

A: Value of a constant function is always same irrespective of input.

Q: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form…

A:

Q: Express the limit as a definite integral. lim xk Ax [-3, 2] 4-0 k 1

A: Given

Q: find the limit as x approaches infinity of (1+2/x)^x

A: Find the limit as x to infinity,

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

A:

Q: lim is: X+ d X Does not exist

A: Use the definition of limit to solve this problem.

Q: Calculate the limit and show proof. lim (1,1)(0,0) r2 + y?

A:

Q: Find limit, or show that it does not exist. 2x²y (x,y)¬(0,0) x*+y2 lim

A: Consider the given: limx, y→0, 02x2yx4+y2Find two different paths to approach the point that gives…

Q: 5. Show that x³y³ lim (x,y) →(0,0) 2x¹2 + 3y4 does not exist.

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Q: Consider the function f (x, y) : 2y Show that lim (x,y)→(0,0) f (x, y) does not exist by ɛ – 8…

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Q: Find the limits in Exercise

A: Given : limh→055h+4+4

Q: B. Calculate the limits of the following functions.. 1. limx¬-1(2X2 + X + 4) 2. limy--2(y3 + 5y – 1)…

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Q: Show that the limit doesn't exis 3x2 1) (x,y)→(0,0) x² + y² lim 2) (х,у

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Q: (b) Show that lim (x.y)(0,0) 2x6 + y2 does not exist by letting (x, y)→(0, 0) along the curve y =…

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

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Q: sec lim x→1+ Vx7-1

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Q: Show that the limit of the function does not exist xy lim (xy)-(0,0) x2 + y?

A: We have to show that limit of the function does not exist.

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: x-y (x,y) →(0.0) x + y 2.) Prove that lim does not exist.

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Q: Find the Limit et – 1 lim t→0+ t3

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Q: If [ f(x)\dx<∞ show that limf(x)dx=0 k→∞00 1

A: We have to prove that given expression.

Q: 4x 24. lim x→1/4 tan x

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

A: Given

Q: Show that xy lim (x,y)→(0,0) x2 + y8 does not exist.

A: If two different path have two different limit then limit does not exist . Now find the limit along…

Q: 6ln (1+x) lim х>0 2е3х—2secx

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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 the limits limx→0+x (ln x)2

A: Consider : limx→0+x(ln2x). Modify the limit function. limx→0+(ln2x)1x…

Q: 2. Use Squeeze Theorem to find lim, x f(z), if for all z > 4 Ge² – 15 < {r) f(x) < VE-2 2e

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Q: Show that the limit does not exist. xy? lim (x,y)→(0,0) x3 + y6

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Q: S (2t)*dt lim x→ =? х* — 1

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Q: 4x2+5y²+- lim (x,y)→(1,-2) 4x²-5y2+e

A:

Q: Find the limit as x approaches negative infinity of (xe1/x-x)

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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…

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

A: Limit is the value of the expression as the independent variable approaches certain value, not…

Q: Find the limit as x approaches infinity of the function V2 – x2 h(x) х3 — х + 1

A: Given:  h(x)=2-x2x3-x+1h(x)=x2 2x2-1x31x3-1x2+1  (Taking highest power of x in the…