Use a computer algebra system to graph the function. f(x, y) = бху x2 + y2 + 14 0.5 -0.5 -1 -2 8e+31 6e+31- Z4e+31- 0.5 2e+31 -0.5 -2 -13 -2 -2 22 lim Find (х, у) — (0, 0) f(x, y) (if it exists). (If an answer does not exist, enter DNE.)

Q: Find the required limit or indicate that it does not exist. 1. lim3(2(t – 3)²i – 7t°j) 2. lim→1(i -…

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Q: Show that the function has no limit as (x,y)→(0,0) f(x,y)=x4/(x4+y2)

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Q: Evaluate the limit. Leave results in exact form. V9 + 7r2 lim 11 + 3x

A: This question is based on limits of inf/inf form.

Q: Q.3 Find the following limits: x+3 3.1 lim→-3 x2+4x+3 x² +4x+3 x+2 3.2 limx-2 Jx² +5-3 u-1 3.3 lim-1…

A: As per the company guidelines we can solve first three parts . I hope that the given solution will…

Q: Find the limit lim Vz +1 Enter I for o0, -I for-oo, and DNE if the limit does not exist. Answer

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Q: 4! find lim, B4,-2) S x approachesto I from postve direction.

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Q: Find the limits in Exercises 1- 3x2 – y² + 5 (x, y)→(0,0) x² + y² + 2 2. (x, y)→(0,4) Vy 1. lim lim

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Q: Consider the graph of y = x2/3 = Vx² on the interval [0, 0]. FIGURE 2. The curve y = x2/3. 2 - Show…

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Q: Use the Squeeze Theorem to prove that lim (r.y)→(0,0) x +y² 0.

A: Using Squeeze Theorem to prove that lim(x,y)→(0,0)x4yx4+y2

Q: Along the path z= e find 2. lim (2,4)→(1,0) y-4zy 3x-y-3

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

Q: Find the limit of the exercise below.

A: Factor the numerator using a^2-b^2=(a+b)(a-b) formula. With a=t and b=4

Q: Find the limit z3 + 4'iz? lim z→4i z2 + 4?

A: We will simplify given function using factoring it to find limit

Q: Among the solutions of the 3rd order linear ODE y" – y" + y' – y = 8et, only one function satisfies…

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Q: I+ 3r2 lim z+00 4x –1

A: To determine :  The limits of  (a) limx→∞x+3x24x-1   (b)  limx→-∞1+4x62-x3

Q: Evaluate f(-1+h) – f(-1) lim where f(r) = 5z'+1. Enter I for oo, -I for -oo, and DNE if the limit…

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Q: Find the limit. 5xz - 7xy P (1, - 1, 0) x2 + y2 - z2 lim %3D O 5 7/2

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Q: 16x4+9y12 (x,y) (0,0) 4x²+3y6 Show that lim does not exist.

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Q: find the orthogonal trajection of the family of curves x2+y2=a2

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

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Q: Find the limit (1+h)3 –1 lim h h→0

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Q: Find the limit: o-4t 6. lim t→0 4 – 13' 17 + t to

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Q: g4 – 2y² f (x, y) as (x, y) → (0,0 x2 + y2

A: Given that: f(x, y)=x4-2y2x2+y2

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

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Q: パーy (x.y)-(0,0) x + y 2.) Prove that lim does not exist.

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Q: x² + y2 lim (x.y)-(0,0) x² + y²

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

Q: Evaluate this path limit: 4.xy3 =??? lim (x, y)¬(0, 0) 2x² +y6 x=y3

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Q: Show with e and 8 that lim (t2 – t – 1, t? – 2t – 2) = (5,6) t→-2

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Q: Show that for any e > 0 and S, 1X₁, lim P(|S₁-81 ≥ 2) = 0. y'a 3140

A: We will use Chebychev's inequality to find the required limit of probability.

Q: Calculate the limit x – y + 4vx – 4Vy Vx - Vy lim(x.y) → o(0,0) | Choose an option: a) -4 b) 0 c)…

A: Answer

Q: If lim | f(x)dx does not exist, b00 a then | f(x)dx diverges. a Select one: False True

A: True  Improper integral said to be convergent if the limit is finite and that limit is the value of…

Q: Find the orthogonal trajection of the family of curves x2+y2=a2

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Q: Select ALL horizontal and vertical asymptotes if the exist (0/10 Puan) f (x) 3x+2 (x-1)(x+5) !! U x…

A: Given  f(x)=3x2+2(x-1)(x+5)

Q: 16x4+9y12 (x,y)→(0,0) 4x²+3y6 Show that lim does not exist.

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Q: Evaluate 3t 9 lim t00 Vt2 - 9t +5 Enter I for oo, 4 for -oo, and DNE if the limit does not exist.…

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Q: f'(0) = Is f(1.5)>0? ('Yes on not) lim fCh-)-f(-)

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Q: tan z lim is Select one: a. e b. 0 с. 1 d. -1

A: Given limx→01xtan(x)

Q: Use a computer algebra system to graph the function. 7xy f(x, y) = x + y2 + 6 3e+31 2.5e+31 20+31 3…

A: We have to graph the function first

Q: Consider the function 2+2+17-2ry+v² if (r, y) # (0,0) f(r,y) = if (1, y) = (0,0). (b) Find…

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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: Consider the function f (x) = x(Va – 1), where a > 0, x > 0. If 0 < a < 1, show that limx0f (x) is a…

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Q: Ex let yct) soluton to the I.V.P y"-y'-2oy=0, yco) =3 , yto) = b If . Lim yL)= O find b?

A: Explanation of the answer is as follows

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

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Q: Find the limit. lim (t i - 7 j+1² k) t-5 lim (t i- 7j+? k) = i i+ i j+ i k

A: To find the limit of the given vector valued function.

Q: Show for the function has no limit as (x,y) → (0,0) f(x, y) 5y3 x°+2y3

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) (t + Δ)2-3(t + Δ) +…

A: The derivative of the function is calculated as follows.

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

Q: What is lim ZH00 2+1 4z2 A -2 в c) D) 1 E) The limit does not exist. 1/4

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Q: For the function f(z) = 4x + 19z + 28, find f'(x) using the f(x +h)- f(x) definition lim O 8% O 38z…

A: Here we will find f'(x) using the given definition.

Q: 2x Sí“(2t-2)² dt (a) Find the limit (if exist): lim 1 2х-1

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