The number of intersection points of the function fx-sin x - y-0-5 ina- x- 0-3-b- x- -6-6- respectively are-

Given two functions f(x)=sin x & y=0.5 Let's consider the first region i.e. x∈ 0, 3π) It can be represented as: Thus, y=0.5 cuts the function y=sin x at 4 ...

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Standard XII

Mathematics

Graphical Interpretation of Differentiability

The number of...

Question

The number of intersection points of the function $f (x) = sin x & y = 0.5 in$
$(a) . x \in (0, 3 π)$
$(b) . x \in [- 6 π, 6 π]$ respectively are:

6, 10

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4, 10

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4, 12

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6, 12

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Solution

The correct option is C $4, 12$
Given two functions $f (x) = sin x & y = 0.5$
Let's consider the first region i.e. $x \in 0, 3 π)$
It can be represented as:

Thus, $y = 0.5$ cuts the function $y = sin x$ at 4 points in the region $x \in (0, 3 π) .$
Now, let's look at the second region i.e. $x \in [- 6 π, 6 π]$

Thus, $y = 0.5$ cuts the function $y = sin x$ at 12 points in the region $x \in [- 6 π, 6 π] .$

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Similar questions

Q. The number of intersection points of the function

f (x) = c o s x

and

y = 1 / 3

in :

(a) x \in (0, 3 π)

(b) x \in [- 3 π, 2 π]

are respectively:

Q. If

f (x)

is an integrable function in

(\frac{π}{6}, \frac{π}{3})

and

I_{1} = \int_{π / 6}^{π / 3} {sec}^{2} x f (2 sin 2 x) d x

and

I_{2} = \int_{π / 6}^{π / 3} c o {sec}^{2} x f (2 sin 2 x) d x,

then:

Q. Assertion :

\int_{π / 6}^{π / 3} \frac{1 d x}{1 + \sqrt{cot x}} = \frac{π}{2}

Reason:

\int_{π / 6}^{π / 3} \frac{f (x) d x}{f (x) + f (\frac{π}{2} - x)} = \frac{π}{12}

Q. Evaluate :

\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{\sqrt{sin x}}{\sqrt{sin x} + \sqrt{cos x}} d x

Q. If

J = π / 3 \int π / 6 \frac{d x}{\sqrt{cos x} + \sqrt{sin x}}

then

π / 3 \int π / 6 \frac{x d x}{\sqrt{cos x} + \sqrt{sin x}}

equals

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The number of intersection points of the function f(x)=sinx & y=0.5 in (a). x∈ (0,3π) (b). x∈[−6π,6π] respectively are:

The number of intersection points of the function $f (x) = sin x & y = 0.5 in$
$(a) . x \in (0, 3 π)$
$(b) . x \in [- 6 π, 6 π]$ respectively are: