If y-2 x 3 -2 x 2 -3x-5- then for x-2 and - x-0-1 value of - y is

The correct option is B 1.9 Given y=2 x ^ 3 2 x ^ 2 +3x 5 ⇒ dy dx =6 x ^ 2 4x+3 ⇒( dy dx #160;) #160;_ x=2 =24 8+3=19 ∵ Δ ...

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Standard XII

Mathematics

Existence of Limit

If y=2 x 3 ...

Question

If $y = 2 x^{3} - 2 x^{2} + 3 x - 5$ , then for $x = 2$ and $Δ x = 0.1$ value of $Δ y$ is

2.002

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1.9

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Solution

The correct option is B $1.9$
Given $y = 2 x^{3} - 2 x^{2} + 3 x - 5$
$\Rightarrow \frac{d y}{d x} = 6 x^{2} - 4 x + 3$
$\Rightarrow {(\frac{d y}{d x})}_{x = 2} = 24 - 8 + 3 = 19$
$∵ Δ y = {(\frac{d y}{d x})}_{x = 2} Δ x$
$\Rightarrow Δ y = 19 \times (0.1) = 1.9$

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If y=2x3−2x2+3x−5, then for x=2 and Δx=0.1 value of Δy is

The correct option is B 1.9Given y=2x3−2x2+3x−5⇒dydx=6x2−4x+3⇒(dydx)x=2=24−8+3=19∵Δy=(dydx)x=2Δx⇒Δy=19×(0.1)=1.9

If $y = 2 x^{3} - 2 x^{2} + 3 x - 5$ , then for $x = 2$ and $Δ x = 0.1$ value of $Δ y$ is

The correct option is B $1.9$
Given $y = 2 x^{3} - 2 x^{2} + 3 x - 5$
$\Rightarrow \frac{d y}{d x} = 6 x^{2} - 4 x + 3$
$\Rightarrow {(\frac{d y}{d x})}_{x = 2} = 24 - 8 + 3 = 19$
$∵ Δ y = {(\frac{d y}{d x})}_{x = 2} Δ x$
$\Rightarrow Δ y = 19 \times (0.1) = 1.9$