Question

f(x) = cos x + sin x if x ≥ 0 (and) x + k if x<0 . Find value of k if limx—›0 exists​

Answer 1

Answer:

Let u = f (x) and v = g (x) be two functions of x, then to find ... k = 1. Thus, f is continuous at x = 0 if k = 1. Example 2 ... Example 16 If f (x) = |cos x – sinx|, find f ...

Answer 2

The value of k=1 when lim x tends to 0 exist.

Step-by-step explanation:

$f(x)=cosx+sinx$ if $x\geq0$

$f(x)=x+k$ if x<0

When x tends to zero then limit exist

When limit exits

Then, RHL=LHL

$\lim_{x\rightarrow 0+}f(x)=\lim_{x\rightarrow 0-}f(x)$

$\lim_{x\rightarrow 0+}(cosx +sin x)=\lim_{x\rightarrow 0-}(x+k)$

$cos 0+sin 0=0+k$

$1+0=k$

By using $cos 0^{\circ}=1, sin 0=0$

$k=1$

Hence, the value of k=1 when lim x tends to 0 exist.

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