(b) Show that lim (z.)(0,0) lim (z.)(0,0) does not exist. (c) Show that does not exist if +: < 1, where m, n > 0, p and q are even numbers. Hint: if p > q, consider the curve y = r.

Q: 2(x-1)* - y² Lex-1)* +2y (d) Show lim does not exist.

A: Limit exist

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A:

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

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A:

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A:

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A:

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A:

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A:

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A:

Q: Find the limit and discuss the continuity of the function.

A: The function is given as,

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A:

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A: Here, we have to reduce this limit to a limit in a single variable by using the equation of curve.…

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A: Show thatlimx,y→0,0z-x2+y24-16-x2-y2-z2=0

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A:

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A: a)

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A:

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A:

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A:

Q: Show that lim (2,v)>(0,0) **+y D0.

A:

Q: Find the limits in Exercise

A: Given,

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A:

Q: 3. Show that lim(r.y)→(0,0) xy =0. (Hint: Use the fact the y| = Vy² and therefore y|< Vx² + y²)

A:

Q: x² + y2 lim (x.y)-(0,0) x² + y²

A: Consider the limit  limx,y→0,0x2+y2x2+y2

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A: Given yx=x2-2x-2           P3,1

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A:

Q: Use the graphs of f and g and their tangent lines at (2, 0) to find lim f(x) x+2 g(x) y4 y = 1.6(x -…

A: We need to evaluate the value of limx→2f(x)g(x) using the following graph

Q: hey you didnt state the assumptions of the model and the limintations as well

A: To state: Assumptions and limitations of an exponential model.

Q: tar lim x² + vZ 2 (x,V) → (0,0) x2+ y?

A: Given lim(x,y)→(0,0)etan(xy)-1x2+y2 To prove the existence. use the sequential criteria for  That is…

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A: Given: limθ→π4tanθ-1θ-π4

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A:

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A:

Q: 8) Find the limit (exact value) a) lim Vy - 3y – y ytoo tan ax b) lim- x→0 sin bx (a ±0,b± 0)

A:

Q: Prove, using the formal definition, that lim→-1 (T+1)² +0o. %3D

A: We have to find the limit limx→-13x+12=+∞.

Q: Q3 (A): By using "L' Hopital rules"; Find the limits of: (1) lim, al 1-00 *24² (2) Lim, x³(tan¹x-x)

A: L'Hospital Rule : According to L'Hospital Rule,if we have an undetermined form of 00 or ∞∞, then we…

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A:

Q: Along the path a = e" find %3D lim (7,y) (1,0) y²-6ry 3r-y-3 O 2 O -2 O-3 O does not exist 0 3

A: we have to find the following limit

Q: cz+ 2) Use the definition of limit t. prove; lim 2=4 22

A:

Q: The graph of fCx) below To evalvate tue following limits. Ao lim fex) 104 9. B. ling fCX) C.lim f(X)…

A: Given, graph of fxTo find: limx→2-fx limx→2fx limx→4fx limx→5fx limx→∞fx

Q: Find the limit or show that it does not exist

A: To find:

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A:

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A:

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A: Given limx→01xtan(x)

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A:

Q: Shone that lim g (x,yJ-p (0,0) does not exist,

A: According to the definition of limit, we have

Q: Use the definition for the slope of a tangent line below to explain how slopes of secant lines…

A: Assume 2 points ( a,f(a) ) and ( x,f(x) ) such that ( x,f(x) ) is any point near ( a,f(a) ).The…

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A:

Q: Зу Let flx,y) = , find the lim(xy)¬(-1,1)( Зу %3D x+y' ) along the curve y=x² .

A:

Q: F(x) Let F(r) = | 3e" dt. Find lim if it exists. If the limit does not exist, explain why.

A:

Q: e-²-y² – 1 lim (7,y)→(0,0) x2 + y²

A: To find limit using polar coordinates limx,y→0,0e-x2-y2-1x2+y2