Dy - dx -lim - x - 0 - y - xA- TrueB- False

The correct option is A True Recall what was discussed in the videos. The operator dy/dx gives ratio of change in y coordinate to the change in x coordinate w ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Derivative Operator dy/dx

dy / dx =lim ...

Question

$\frac{d y}{d x} = l i m_{Δ x} \to 0 \frac{Δ y}{Δ x}$

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A True
Recall what was discussed in the videos. The operator $\frac{d y}{d x}$ gives ratio of change in y coordinate to the change in x coordinate when the change in x coordinate is infinitesimally small . That infinitesimal change in x in denoted by taking the limit of change in x as 0. Which means change in the x value tends to zero and is very very small. So the above statement is true

Suggest Corrections

Similar questions

\frac{d y}{d x} = l i m_{Δ x} \to 0 \frac{Δ y}{Δ x}

\frac{d y}{d x} = x^{2} + y^{2}

is a homogeneous differential equation.

Q. For the function y = f(x) the formal definition of derivative is

f^{'} (x) = {lim}_{Δ x \to 0} f (X + Δ X) - f (X) .

Q. As per the chain rule if y is a function of t and t is a function of x, then

\frac{d y}{d x} = \frac{d y}{d t} \times \frac{d t}{d x} .

For a function given by $y = f (t) and x = g (t)$ . Then $\frac{d y}{d x}$ can be expressed as
$\frac{\frac{d f (t)}{d t}}{\frac{d g (t)}{d t}}$

Join BYJU'S Learning Program

dydx=limΔx→0ΔyΔx

$\frac{d y}{d x} = l i m_{Δ x} \to 0 \frac{Δ y}{Δ x}$