2xy3 lim (xy)-(0,0) x² + 2y6

Q: 3r²-7r-6 lim r2 - 9 6.

A: We have to evaluate the limit 11) limx→33x2-7x-6x2-9 12) limx→25x-25x-5

Q: limx→∞x3+26x2−x=

A:

Q: lim,-2 3x? – x – 7 |

A: Applying limit property

Q: 2x + 1 (b) √ ² (1 − x) -dx

A:

Q: Vx+3x² limx¬0 X→∞ 4х-1

A:

Q: x2 + 5 2. lim 9x4+2x+4

A: limx->∞x2+59x4+2x+4

Q: Calculate limx→∞(√x2+1−√x2−1).

A: The limit of any function at any point x=a is the value which the function has tendency to acquire…

Q: lim (412 + 8t – 5)3/2 t- 2.

A:

Q: x2-4x+4 2. lim x-2 x2-x-2

A:

Q: lim V8+X -2

A:

Q: lim У-у-г уг -30+2 зу Уже

A: We have to findlimx→−2

Q: 5x' +8x² lim x→0 3x* – 16 r? 3

A: Cancel out the common factor from numerator and denominator than put the x and calculate limit.

Q: lim (4t – 2at + 3a) →-1

A: We plug t=-1

Q: lim (4x2 + 2x + 5) = 5x→0

A: We will plug x=0 in place of x

Q: (d) lim LI-IX √x²+2x+1 x² - 1

A:

Q: 4х+2 1. lim 9x² -3 2

A:

Q: The value of lim (x³+2x4- 7x3- 5x²+ 11x – 15) X--2 (A) - 1 B) 1 2 (D -5

A: We need to evaluate limx→-2 x5+2x4-7x3-5x2+11x-15

Q: Vx²+1 +5x lim 2x+3 X→ -0 -1 3 1 2 1 2

A:

Q: Vx² + 1 +x lim X ∞ 4xr -1 II

A:

Q: x² + 7x- 18 lim 6- 1 -69

A: Given

Q: 3- 5V+811 lim -00 2/2+2-162 t3-5v

A: After initial observation, I can see there is difference of variable in the limit 'x' and variable…

Q: 2r2 - 4z lim r2-2r-15

A: Given,         limx→-3-2x2-4xx2-2x-15

Q: Vx2 + a? lim Væ2 + 62 Væ2 + c2 Væ2 + d?

A:

Q: Jx²+2 Lim X-7 3x -6

A:

Q: x2-2x4メ4x Lim (X-1)²+ y2 2 2 .

A: Solve using  properties of the limits

Q: Find y (x +5x)*(x + sec x)5

A: Differentation by two products

Q: 5x2 + 3 lim x → 1 x² + 6x – 4

A: Concept- limit x tend to 1 ,that means substitute the value of x=1 .

Q: 4х-8 lim Jx² +16

A: Try to put 'x' in denominator , so that when x tends to infinity then that term will become zero.

Q: (d). Lim    x +6x3     x →0   4x + 7x²

A:

Q: . lim e²x-1 X30 3x+4 sinx

A: given limit is of 00 indeterminate formso, apply the L'Hospital's rule to solve the limit

Q: e*+3x-4 mx→0 3x+1

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.