2x^3-3x^2+kx-1 is divided (x-1),the remainder is 2 find k

Mathematics

1 answer:

Debora [2.8K]2 years ago

7 0

Answer:

k = 4

Step-by-step explanation:

if f(x) is divided by (x - h) then f(h) is the remainder

f(x) = 2x³ - 3x² + kx - 1

divided by (x - 1) , so h = 1 , then

2(1)³ - 3(1)² + k(1) - 1 = 2

2 - 3 + k - 1 = 2

- 2 + k = 2 ( add 2 to both sides )

k = 4

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a) So, this integral is convergent.

b) So, this integral is divergent.

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Step-by-step explanation:

We calculate the next integrals:

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$\int_1^{2}\frac{dz}{(z-1)^2}=\left[-\frac{1}{z-1}\right]_1^2\\\\\int_1^{2}\frac{dz}{(z-1)^2}=-\frac{1}{1-1}+\frac{1}{2-1}\\\\\int_1^{2}\frac{dz}{(z-1)^2}=-\infty\\$

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