Verify Rolle's theorem for each of the following functions:

Question: Verify Rolle's theorem for each of the following functions: $f(x)=x^{2}-4 x+3$ in $[1,3]$ Solution:...

Verify Rolle's theorem for each of the following functions:

Question: Verify Rolle's theorem for each of the following functions: $f(x)=x^{2}-5 x+6$ in $[-3,6]$ Solution:...

Verify Rolle's theorem for each of the following functions:

Question: Verify Rolle's theorem for each of the following functions: $f(x)=x^{2}-5 x+6$ in $[2,3]$ Solution:...

Verify Rolle's theorem for each of the following functions:

Question: Verify Rolle's theorem for each of the following functions: $f(x)=x^{2}-x-12$ in $[-3,4]$ Solution:...

Verify Rolle's theorem for each of the following functions:

Question: Verify Rolle's theorem for each of the following functions: $f(x)=x^{2}$ on $[-1,1]$ Solution:...

Solve this following

Question: If there is an error of $0.1 \%$ in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere. Solution:...

Show that the relative error in the volume of a sphere, due to an error

Question: Show that the relative error in the volume of a sphere, due to an error in measuring the diameter, is three times the relative error in the diameter. Solution:...

Question: The radius of a sphere shrinks from $10 \mathrm{~cm}$ to $9.8 \mathrm{~cm}$. Find approximately the decrease in (i) volume, and (ii) surface area. Solution:...

Solve this following

Question: The pressure $\mathrm{p}$ and the volume $\mathrm{V}$ of a gas are connected by the relation, $\mathrm{p} \mathrm{V}^{1 / 4}=\mathrm{k}$, where $\mathrm{k}$ is a constant. Find the percentage increase in the pressure, corresponding to a diminution of $0.5 \%$ in the volume. Solution:...

If the length of a simple pendulum is decreased

Question: If the length of a simple pendulum is decreased by $2 \%$, find the percentage decrease in its period $\mathrm{T}$, where $\mathrm{T}=2 \pi \sqrt{\frac{1}{\mathrm{~g}}}$. Solution:...

A circular metal plate expands under heating so that its radius increases

Question: A circular metal plate expands under heating so that its radius increases by $2 \%$. Find the approximate increase in the area of the plate, if the radius of the plate before heating is $10 \mathrm{~cm}$. Solution:...

Solve this following

Question: If $y=\sin x$ and $x$ changes from $\frac{\pi}{2}$ to $\frac{22}{14}$, what is the approximate change in $y$ ? Solution:...

find the approximate values of

Question: find the approximate values of $\cos 61^{\circ}$, it being given that sin $60^{\circ}=0.86603$ and $1^{\circ}=0.01745$ radian Solution:...

find the approximate values of

Question: find the approximate values of $\log _{10}(4.04)$, it being given that $\log _{10} 4=0.6021$ and $\log _{10} e=0.4343$ Solution:...

find the approximate values of

Question: find the approximate values of $\log _{e} 10.02$, given that $\log _{e} 10=2.3026$ Solution:...

find the approximate values of

Question: find the approximate values of $\frac{1}{(2.002)^{2}}$ Solution:...

Using differentials, find the approximate values of: Find the approximate values of

Question: Using differentials, find the approximate values of: Find the approximate values of $\sqrt[4]{15}$ Solution:...

Using differentials, find the approximate values of:

Question: Using differentials, find the approximate values of: Find the approximate values of $\sqrt{49.5}$ Solution: $\Rightarrow \sqrt{4} 9.5=7.0357$...

How many times constants will elapse before the charge on a capacitor falls to

Question: How many times constants will elapse before the charge on a capacitor falls to $0.1 \%$ of its maximum value in a discharging RC circuit? Solution:...

Using differentials, find the approximate values of

Question: Using differentials, find the approximate values of: Find the approximate values of $\sqrt{0.24}$ Solution:...

Using differentials, find the approximate values of: Find the approximate values of

Question: Using differentials, find the approximate values of: Find the approximate values of $\sqrt{27}$ Solution:...

Using differentials, find the approximate values of:

Question: Using differentials, find the approximate values of: Find the approximate values of $\sqrt[3]{29}$. Solution: $\Rightarrow \sqrt[3]{29}=3.074$...

How many times constants will elapse before the current in a charging RC

Question: How many times constants will elapse before the current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging $\mathrm{RC}$ circuit. Solution:...

A 100μF capacitor is joined to a 24V battery through a 1.0MΩ resistor.

Question: A $100 \mu \mathrm{F}$ capacitor is joined to a $24 \mathrm{~V}$ battery through a $1.0 \mathrm{M} \Omega$ resistor. Plot qualitative graphs (a) Between current and time for the first 10 minutes and (b) Between charge and time for the same period Solution:...

A parallel-plate capacitor has plate area

Question: A parallel-plate capacitor has plate area $20 \mathrm{~cm}^{2}$, plate separation $1.0 \mathrm{~mm}$ and a dielectric slab of dielectric constant $5.0$ filling up the space between the plates. This capacitor is joined to a battery of emf $6.0 \mathrm{v}$ through a $100 \mathrm{k} \Omega$ resistor. Find the energy of the capacitor $8.9 \mu$ after the connections are made. Solution:...