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3 years ago

Y=

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

7 0

Answer:

(1) e2x [ (2x -1 )cot x – x cosec2x]/x2

(2) e2x [ (2x +1 )cot x – cosec2x]/x2

(3) e2x [ (2x -1 )cot x + cosec2x]/x2

(4) none of these

Solution:

Given y = e2x cos x /x sin x

Differentiate w.r.t.x

Use quotient rule

dy/dx = [x sin x (d/dx)e2x cos x – e2x cos x (d/dx) x sin x]/ (x sin x)2

= [x sin x (e2x ×2× cos x – e2x sin x ) – e2x cos x ( sin x+ x cos x)]/ (x sin x)2

= [ x 2 sin x cos x e2x – e2x x sin2 x – e2x cos x sin x – e2x x cos2 x]/ (x sin x)2

= [ x sin 2x e2x – x e2x(sin2x+cos2x) – e2x sin x cos x]/(x sin x)2

= [ x e2x sin 2x – x e2x – e2x sin x cos x]/(x sin x)2

= [ 2x e2x cot x – x e2x cosec2 x – e2x cot x]/x2

= e2x [ 2x cot x – x cosec2 x – cot x]/x2

= e2x [ (2x -1 )cot x – x cosec2x]/x2

Hence option (1) is the answer

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3 years ago

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saw5 [17]

Here is your answer

Both

a) /_D

c) /_ADB

are correct

REASON:

/_ADB represents an angle between AD and BD which is marked in the question.

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[However writing a single letter to represent an angle is not completely correct. But when there is only one angle represented through the point then writing a single letter is correct

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shepuryov [24]

Answer:

Step-by-step explanation:

Note that in this diagram, point A represents point X, point B represents point Y, and point C represents point Z.

From the diagram, it appears as if $\overline{XZ} \perp \overline{XY}$ . To determine if this is the case, we can find the slopes of both segments.

$m_{\overline{XZ}}=\frac{4-1}{4-1}=1\\m_{\overline{XY}}=\frac{-1-1}{3-1}=-1$

Since these slopes are negative reciprocals, we know that they are perpendicular.

This means we can use the formula $A=\frac{1}{2}bh$ , where b is the base (XY) and h is the height (XZ).

Note these are interchangeable.

Using the distance formula,

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