A function is defined as f x - sin x-x- x 0- If x- 0Ltf x exists- then find a- b and the limit-

The correct options are B b=1 C a may be any real number. D limit=1 R.H.L. = L.H.L. h→ 0limsin ( 0 h )/ ( 0 h )= h→ 0limsin h/h= 1 ...

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Substitution Method to Remove Indeterminate Form

A function is...

Question

A function is defined as $f (x) = {\begin{matrix} \frac{sin x}{x}, & x < 0 a x + b, & x > 0 \end{matrix}$ If $L t x \to 0 f (x)$ exists, then find $a, b$ and the limit.

a = 1

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b = 1

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l i m i t = 1

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a

may be any real number.

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f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{e^{\frac{1}{x}} - 1}{e^{\frac{1}{x}} + 1} x \neq 0 0 x = 0 \end{matrix}

f (x)

f (x) = ⎧ ⎨ ⎩ \begin{matrix} x + a; x < 0 x; 0 \leq x < 1 b - x; x \geq 1 \end{matrix}

f (x)

a + b

f : [0, \infty] \to R

f (x) = {\begin{matrix} | x - a | - 1, & 0 \leq x < 2 b (x - 2)^{2}, & x \geq 2 \end{matrix}

a

b

a ϵ (0, 2)

b \neq 0

f (x)

[a, b]

f (x) \geq 0

x \in [a, b]

(b - a) lim n \to \infty \frac{1}{n} [f (a) + f (a + h) . . . f (a + (n - 1) h)]

h = \frac{b - a}{n}

h \to 0

n \to \infty

\frac{1}{x}

\frac{1}{x}

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