TS EAMCET · Maths · Application of Derivatives
The approximate value of \((1.0002)^{3000}\) is
- A \(1.2\)
- B \(1.4\)
- C \(1.6\)
- D \(1.8\)
Answer & Solution
Correct Answer
(C) \(1.6\)
Step-by-step Solution
Detailed explanation
Let \(y=f(x)=x^{3000}\) here \[ \begin{aligned} x & =1, \Delta x=0.0002 \\ \Delta y & =f^{\prime}(x)=3000 x^{2999} \Delta x \\ \Delta y & =(3000)(0.0002)=0.6 \\ f(x+\Delta x) & =y+\Delta y=1+0.6=1.6 \end{aligned} \]
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(|\bar{a}|=4,|\bar{b}|=5,|\bar{a}-\bar{b}|=3\) and \(\theta\) is the angle between the vectors \(\overline{\mathrm{a}}\) and \(\overline{\mathrm{b}}\), then \(\cot ^2 \theta=\)TS EAMCET 2023 Easy
- The line \(4 x+3 y-4=0\) divides the circumference of a circle in the ratio \(1: 2\). If \(\mathrm{C}(5,3)\) is the centre of that circle, then equation of the circle isTS EAMCET 2022 Medium
- If the roots of the equation exceed , thenTS EAMCET 2018 Easy
- If thenTS EAMCET 2021 Easy
- Two chords of the circle \(x^2+y^2-2 g x-2 h y+g^2+h^2-c^2=0\) are passing through the point \((g, h+c)\) and the line \(y=x\) bisects these two chords. ThenTS EAMCET 2019 Hard
- \(\begin{aligned} & \text { If } \int \frac{1}{\operatorname{cosec} x+\cos x} d x=\frac{1}{2 \sqrt{3}} \log |f(x)| \ & -\int \frac{\cos x-\sin x}{2+\sin 2 x} d x+c \text { then at } x=\frac{\pi}{3},|f(x)|=\end{aligned}\)TS EAMCET 2023 Medium
More PYQs from TS EAMCET
- Two identical blocks \(A\) and \(B\), each of mass \(m\) resting on smooth floor, are connected by a light spring of natural length \(L\) and the spring constant \(k\), with the spring at its natural length. \(A\) third identical block \(C\) (mass \(m\) ) moving with a speed \((v)\) along the line joining \(A\) and \(B\) collides with \(A\). The maximum compression in the spring is proportional toTS EAMCET 2003 Hard
- If \(B_V\) and \(B_H\) are respectively the vertical and horizontal components of the earth's magnetic field at a place where the angle of dip is \(60^{\circ}\), then the total magnetic field at that place isTS EAMCET 2025 Medium
- If \(A\) and \(B\) are two independent events such that \(P(B)=\frac{2}{7}\) and \(P\left(A \cup B^C\right)=0.8\), then \(P(A \cup B)\) \(=\)TS EAMCET 2018 Easy
- A point on the plane that passes through the points \((1,-1,6),(0,0,7)\) and perpendicular to the plane \(x-2 y+z=6\) isTS EAMCET 2017 Medium
- The lengths of the sides of a triangle are 13 , 14 and 15 . If \(R\) and \(r\) respectively denote circumradius and inradius of that triangle, then \(8 R+r=\)TS EAMCET 2017 Medium
- If \(\int_0^3\left(3 x^2-4 x+2\right) d x=k\), then an integer root of \(3 x^2-4 x+2=\frac{3 k}{5}\) isTS EAMCET 2023 Easy