b2 - a2 Prove that x dx = lim b- a n- 00 b - a + a(b – a) (1) + (6 – a)² ( = lim n² (b - a)2 n2 = lim 36 - a). n- 00 = a(b - a) + lim (b - a) n- 00 = a(b - a) + - a) ])) a+ = (b -

Q: 2. lim (x-7x²-3)

A: We have to find  y= lim   f(x) = lim  (x3 -7x5 -3)      x-> -♾️      x-> -♾️ Indeterminate…

Q: What is the value of lim (1+ 4 )": п 4n O-1+i V2 O 1+i V2 O -1-i V2 1-i V2

A:

Q: 3n Find lim,→0 (1+ )'

A: Here,

Q: x' - 4x? – 9x+36 lim b) x - x-12 x-3 e* -e* – 2x lim c) x- sin x

A: limx→-3x3-4x2-9x+36x2-x-12=limx→-3x2x-4-9x-4x2-4x+3x-12=limx→-3x2-9x-4xx-4+3x-4=limx→-3x2-32x-4x-4x+…

Q: Determine lim X- • ot s/x 7 Sinx

A: limx→0+5x-7sinx

Q: 25) Find: lim,(x²+ax - √x² + bx).

A:

Q: '5x2+3х-1) lim = 4x2+5) n-00

A: Divide the numerator and denominator by the highest power i.e. x^2 and simplify the limit.

Q: let fcx)-x2+てメー1X, five a) limf(x) メ -7 O b) lim f(x) Xー70

A:

Q: date let fcx7= X-3x+2, find al lim fux) X-72 bllim fux) c) lim fox) (1) X-72

A:

Q: If A is an invertible n x n matrix having an eigenvector v and associated eigenvalue A, explain why…

A:

Q: 5x - 1 b) lim Z-+0+ 10z

A: We have to find

Q: 5z 3z (a) Evaluate limz-»00

A: Limit of a function is a value obtained when the variable in a function approaches to some other…

Q: b- Lim (3x³+x²-2/x²+x-2x³+1)

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.