6. For what value(s) of k, does the function f(x) = Ae¹x, where A is some constant, satisfy the following relationship: f"(x) + f'(x)-12f(x)=0

Q: w + 4 w + 10 6. 8.

A:

Q: 4s +5 S -4

A:

Q: lim, 2+ f(x) = →2+ lim 2- f(x) =

A: Given query is to find indicated limit.

Q: 1/3+2/9

A: Given 1/3 + 2/9

Q: 2 3 3 4 6 8

A: The mean is computed below.   Aptitude score(x) Frequency(f) x*f 0 4 0 1 2 2 2 3 6 3 0 0…

Q: 4n – 1

A:

Q: 3 1/4 + 7 1/8

A:

Q: 22n+1 3n+1 2.

A:

Q: 7 11

A:

Q: 1+7/7 + 8

A: Answar would be 10

Q: -8 - 12

A: Given problem is

Q: 4(5+6)=

A: Given: 4(5+6)=

Q: 3/8+5/24

A: The given expression is 3/8 + 5/24.Simplify the given expression as follows.

Q: Expand (a −b)4

A:

Q: 5 L s² + 2s – 3

A: We know that, Laplace transform of 1/(s-1) = e^t

Q: -3 -10

A: The given equation is:  -3   2÷-10    7

Q: limx→- f(x) limo+ f(x) limx→ = = =

A:

Q: V415

A: Given query is to find the square root of 415.

Q: (24) Half the product of a number t and 48

A: The objective is to half the product of a number t and 48.

Q: 4a5b• V18a3b6

A: We have to find

Q: 1+4+6+8

A:

Q: 11 –/7

A:

Q: 8y3 + 216

A:

Q: limx→2 f(x) = lim, ¹x→−1+ f(x) =

A: Given graph of the function fx is   1. Find :  limx→2 fx. 2. Find :limx→-1+ fx.

Q: 2/5 +7/12

A: Please see the answer below.

Q: -2 -4 and D = 4 8

A:

Q: 6 1/6 + 6

A:

Q: 8 15 2 15

A: 8/15 -2/15 here simple substraction given and fraction is given  calculation is given inbelow

Q: Two and two

A: Given:   Two and two

Q: k 24

A: First we solve the inequality. ANd for that , we divide both sides by -6 .And on dividing by…