Use an appropriate definition to prove the following limits. x³ – 16x* = 1 I+0 r°+ 4x² x +2 V9x2 + 4 (a) lim z→5+ x² – 25 (b) lim (c) lim -3 %3D x +2

Q: 3. Find lim (x² + 3x – 18)/(x – 3)-

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Q: CONSIDER THE FOLLOWING FUNCTIONS. f22x+1 AiD gca)= xー1 a) DE TERMINE jG&) =f(x)• g(x) Lim…

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Q: b. Find lim (xv (xVx²+1-x²)

A:

Q: 6х2+1 2. Find lim X→0 V4x4+3x+1

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Q: Evaluate: * х — 5 lim х-5 Vx+4 – 3

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Q: V6 - 5x , x > -1 Determine lim x-2 wheref ( x %3D 2x2 - 5x , x < -1

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Q: 200 (-1) = 1, lim (x – 2) = + Use the results that = 1, lim (x – 2) = +∞ lim I+3 T-1 エ→8 エ→0 to find…

A: Given that limx→∞(x+3x-1)=1and limx→∞(x-2)=+∞Required to…

Q: 4. Evaluate the following limits: 2x2 – 10x + 12 (a) lim x→2 x² – 12x + 20

A: Given: a)  limx→22x2-10x+12x2-12x+20

Q: Find 2-Vx2-5 lim X-1 x+3

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Q: V5x+4-3 3) lim X-1 x-1

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Q: 4. Find lim (x² – 9)/(x² – 8x + 15)

A: To find the limit of given function.

Q: Find Vx² + 8 – 3 lim x--1 x +1

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Q: Vx2 -25 b) lim x→-0o 6x-18

A: We have to find the limit

Q: Show that lim (Vx² +1 – x) = 0. Hint: Observe that 1 Vx² + 1 – x = Vx2 +1 + x

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Q: Find lim (V + 1 - Vĩ).

A: To find the limit

Q: Find Vx2 +8-3 lim X-1 x + 1

A: Limits question

Q: x + 3x – 1 lim V4r6 – 2x エ→ーx 2.r

A: We have to find limit

Q: -2x +x lim x->0 2x+x“ – 2x .3

A: We have to evaluate the limit                                            limx→0x3-2x2+x2x3+x2-2x

Q: Given: lim (x2 + 7x – 5) x→3

A: Let's find.

Q: 5. Find lim [2(a+ h)? – 6(a + h) + 5 – (2a – 6a + 5)]/h h>0

A: Given that, limh→02a+h2-6a+h+5-2a2-6a+5h