Find the value of the following limits: 5y 1-limy→o tan 10y 2-limx-0 6x cot3x 7x²+8x 3-limx-0 4x² V25+x -5 4-limx¬0° sinny 5-limy-1 y-1

Q: Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) -…

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A: Given the term : limx→2 x ∫x21+t2dtx2-4 We need to evaluate it.

Q: 1. lim (x – 4)(x² + 8) x→5 2(t-10)² 2. lim t→10 t

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Q: I. Find the limit of the algebraic functions if it exists. Show your solution analytically. 1.…

A:

Q: 10, elseunére Y= amount ok pollutant Per Sample callected a buve the Stack Wthout the cleaning devie…

A: Given  fy1,y2=1   , 0≤y1≤2 , 0≤y2≤1 , 2y2≤y10   ,  elsewhere

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A:

Q: Evaluate the following limits. 1. lim (1+ Vw)(2 – w² + 3w*)

A: According to our company rules we can answer only the first question and rest can be reposted.

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

A:

Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

A:

Q: x³-7x² +10x x²+x-6 4. lim: x-2 5. lim sin лw w4 w²2²-16

A: The objective of the question is determine the indeterminate form of given limits.

Q: 4 Find lim х — 4 Væ – 2 x→4

A:

Q: Let h(x)

A: hx=x2,      x<23,       x=22,       x>2 Now, The left hand limit at x=2 is,…

Q: lim x + x - 2 Example 15. Evaluate x →1 x' - 3x + 2 2.

A:

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A: Given To check it is exist or not  If it exists then find the value

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A:

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A: We have to solve above question and find  limit

Q: lim ( Vy? – y) y² + y +1 – y00

A: limy→∞y2+y+1-y2-y

Q: valuate 10-Vx a. lim x→100 x-100 b. lim (-2x+4)²–4 1 c. lim *+2 5 x→3 x-3 X-3 3-x

A: Given that:

Q: Find the limits: Vx + 25 – 5 (а) lim т? + 5х + 1 (b) lim x→2 x3 – x – 1 1– sin 0 (c) lim 05 1+…

A:

Q: lim x-3-j 2 x²-8-j6 2x²− x³ −3l+x −j37

A:

Q: Find the value (1) lim (x,y)-(2-3) (3) lim (xy)-(11) √x-√√y of the following limits: x²-2xy + y²…

A: As per the instruction, post the question again for question (5). For (1),    limx, y→2,…

Q: x° +2y² +x*y lim (* ,y') → (0, 0) x* +3y - x*y

A:

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: