Question
The equation of the normal to the curve \(y = 4x^3 + 2 \sin(x)\) at \((0, 3)\) \(y = 4x^3 + 2 \sin(x)\) at \( (0, 3) \)
The correct answer is
x+ 2y=6
Given curve is
\( y = 4x^3 + 2 \sin(x) \) at \( (0, 3) \)\( \frac{dy}{dx} = 12x^2 + 2 \cos(x) \)
Slope tangent at \( (0, 3) \) is 2
So, slope of normal is \( -\frac{1}{2} \)
Equation of normal is
\( y - 3 = -\frac{1}{2}(x - 0) \)\( 2y - 6 = -x \)
\( x + 2y = 6 \)
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Important Questions from Mixed Topics (CUET-UG)
- The area of the region bounded by y=|x-5|, x=0 and x=1 is:
Match List – I with List – II.
List - I
Differential equation
List - II
Integrating Factor (I.F.)
(A) \(\frac{dy}{dx} - \frac{y}{x} = 2x\) (I) \(x^{2} - 1\) (B) \(\frac{dy}{dx} + \left( \frac{2x}{x^2 - 1} \right) y = \frac{2}{(x^2 - 1)^2}\) (II) \(\sqrt{ x^{2}-1 }\) (C) \(\frac{dy}{dx} - \big( \frac{x}{1- x^{2} } )y= \frac{1}{ 1-x^{2} }\) (III) \(\frac{1}{x}\) (D) \(\frac{dy}{dx} + \frac{y}{1 + x^2} = \frac{cotx}{1+ x^{2} }\) (IV) \(1+ x^{2}\) Choose the correct answer from the options given below:
Which of the following statement is incorrect?
Which of the following statement is TRUE?
Which of the following statement is correct?
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