Question

Find the value of k, if the function
f(x)= (1+kx)^1\x for x not = 0
e^5 for x=0
if f(x) is continous at x=0 .
​

Answer 1

1. The constant function, i.e. f (x) = c

2. The identity function, i.e. f (x) = x R

3. The polynomial function, i.e.

f (x)= a0 x

n

+ a1 x

n–1 + ... + an–1 x + an 4. | x – a | (– ∞ , ∞ )

5. x

–n

, n is a positive integer (– ∞ , ∞ ) – {0}

6. p (x) / q (x), where p (x) and q (x) are R – { x : q (x) = 0}

polynomials in x

7. sin x, cos x R

8. tan x, sec x R– { (2 n + 1)

π

2

: n ∈ Z}

9. cot x, cosec x R– { (nπ : n ∈ Z}

Answer 2

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