Question

for what value of lambda (λ) is the following function continuous at x=2?
f(x) = λx+5 when x ≤ 2
= x-1 when x > 2​

Answer 1

⇒

x→0

lim

λ(x

2

−2x)=

x→0

lim

(4x+1)=λ(0

2

−2x0)

⇒λ(0

2

−2⋅0)=4⋅0+1=0

⇒0=1=0, which is not possible

Therefore, there is no value of λ for which f is continuous at x=0

At x=1,

f(1)=4x+1=4⋅1+1=5

x→1

lim

(4x+1)=4⋅1+1=5

∴

x→1

lim

f(x)=f(1)

Therefore, for any values of λ, f is continuous at x=1

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Answer 2

Answer:

Thanks a lot of mate.

Very very thankful to you