Fsc Math part 1 Function and limits pdf

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hamza-mkfa

Chapter 01 Function and Limits important mcqs

Quiz time! Elevate your grasp on Chapter 01 – Functions and Limits. Take the challenge, answer the MCQs, and watch your confidence soar as you master the fundamental concepts. Gud Luck !

Welcome to your Mathematics Quiz

Important Short Questions for Chatper 03

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Fsc part 02

Important Short Questions for Chatper 03


Find \partial{y} and dy if y=x^2-1 when x changes from 3 to 3.02
Find \partial{y} and dy if y=\sqrt{x} when x changes from 4 to 4.41
Find approximate increasse in the volume of a cube if the length of its each edge changes from 5 to 5.02
Evaluate \int{x(\sqrt{x}+1)dx}
Evaluate \int{ (2x+3)^\frac{1}{2} dx}
Evaluate \int{(\sqrt{x}+1)^2 dx}
Evaluate \int{\frac{(3x+2)}{\sqrt{x}} dx}
Evaluate \int{\frac{(\sqrt{θ}-1)^2}{\sqrt{θ}} dθ}
Evaluate \int{\frac{(1-\sqrt{x})^2}{\sqrt{x}} dx}
Evaluate \int{(a-2x)^{\frac{3}{2}} dx}
Evaluate \int{\sqrt{1-cos2x} dx }
Evaluate \int{(lnx)× \frac{1}{x} dx}
Evaluate \int{\frac{1}{1+cosx} dx}
Evaluate \int{cos3x sin2x dx}
Evaluate \int{tan^{2}⁡x dx}
Evaluate \int{\frac{x}{\sqrt{4+x^2 }} dx}
Evaluate \int{\frac{x^2}{4+x^2 } dx}
Evaluate \int{\frac{dx}{x^2+4x+13}}
Evaluate \int{\frac{1}{xlnx} dx}
Evaluate \int{\frac{sec^2⁡x}{\sqrt{tanx}} dx}
Evaluate \int{sin^{2}⁡x dx}
Evaluate \int{\frac{1}{(1+x^2 )} tan^{-1}⁡x dx}
Evaluate \int{\frac{sinθ}{1+cos^{2⁡}θ } dθ}
Evaluate \int{cosx\frac{(ln sinx)}{sinx} dx}
Evaluate \int{\frac{ \sqrt{2}{sinx+cosx} dx}
Evaluate \int{xcosx dx}
Evaluate \int{lnx dx}
Evaluate \int{x lnx dx}
Evaluate \int{tan^{-1}⁡x dx}
Evaluate \int{x^2 sinx dx}
Evalluate \int{x tan^{-1}{⁡x} dx}
Evaluate \int{e^x (\frac{1}{x}+lnx)dx }
Evaluate \int{e^x (cosx+sinx) dx }
Evaluate \int{e^{2x} (-sinx+2cosx)dx}
Evaluate \int{e^{-x} (cosx-sinx)dx}
Evaluate \int{\frac{e^{mtan^{-1} x}}{1+x^2} dx}
Evaluate \int_{-1}^{3}({x^3+3x^2})dx

Evaluate\int_{-1}^{2}{(x+|x|)}dx
Evaluate\int_{1}^{e}{x lnx} dx
Evaluate\int_{-1}^{1}{(x^\frac{1}{3}+1)}dx
Evaluate\int_{-2}^{0}{\frac{1}{(2x-1)^2}} dx
Evaluate\int_{-6}^{2}{ \sqrt{3-x}} dx
Evaluate\int_{2}^{ \sqrt{5}}{x \sqrt{x^2-1}} dx
Evaluate\int_{1}^{2}{\frac{x}{x^2+2}} dx
Evaluate\int{0}^{3}{\frac{dx}{x^2+9}
Evaluate\int_{1}^{2}{lnx} dx
Evaluate\int_{0}^{2}{e^{\frac{x}{2}}-e^-{\frac{x}{ 2}} }dx
Evaluate\int{0}^{\frac{π}{3}}{cos^2⁡θ dθ}
Evaluate\int_{-1}^{5}{|x-3| } dx
Evaluate\int_{\frac{1}{8}}^{1}{\frac{(x^{\frac{1}{3}}+2)^2}{x^{\frac{2}{3}}}} dx
Evaluate\int_{0}^{\frac{π}{4}}{\frac{sinx-1}{cos^2⁡x}} dx

Find the area between the x-axis and the curve y=4x-x^2
Solve the differential equation \frac{dy}{dx}=\frac{1-x}{y}
Solve the differential siny cosecx \frac{dy}{dx}=1
Solve the differential equation \frac{1}{x}\frac{ dy}{dx}-2y=0

Importan short Questions for chap # 02 click here

Important Short Questions for  Chatper 02 Math

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FSc Part 2

Q.No. 1. Differentiate from the first principles if y = x m

Q.No. 2.Differentiate from first principles: y = x 3 / 2

Math Statements

Q no. 3.Find the derivative of Y = ( 2 x + 2 ) ( x – x ) with respect to x.

Q no.4 Differentiate x – 3 + 2 x – 3 2 + 3 with respect to x.

Q no.5 Differentiate a + x a – x with respect to x.

Q no. 6 Differentiate ( x – 1 x ) 2 with respect to x.

Q no. 7 If y = x – 1 x , show that 2 x dy dx + y = 2 x .

Q no. 8 If \( y = x^4 + 2x^2 + 2 \), prove that \( \frac{dy}{dx} = 4x\sqrt{y-1} \).

Q no. 9 Find \( \frac{dy}{dx} \) if \( x = at^2 \) and \( y = 2at \).

Q no.10 Find \( \frac{dy}{dx} \) if \( x^2 + y^2 = 4 \).

Q no.11 Find if \frac{dy}{dx} = \frac{-2y}{2y + 4 - 2x}

Q no.12 Find \(\frac{dy}{dx}\) if y^2-xy-x^2+4=0

Q no.13 Find \( \frac{dy}{dx} \) by making a suitable substitution, if \( y = \sqrt{x + \sqrt{x}} \)

Q no.14 Find \( \frac{dy}{dx} \) by making a suitable substitution, if \( y=(3x^2-2x+7)^6 \)

Q no.15 Find \(\frac{dy}{dx}\) if 3x+4y+7=0

Q no.16 Find \(\frac{dy}{dx}\) if xy+y^2=2

Q No.17 Find \(\frac{dy}{dx}\) if x^2-4xy-5y=0

Q No.18 Find \(\frac{dy}{dx}\) if x=\theta+\frac{1}{\theta} and y=\theta+1

Q.No.19. Differentiate ((1+x)^2)^n with respect to x^2

Q No. 20 If y=tan(2{\tan^{-1}⁡\frac{x}{2}}) , show that \frac{dy}{dx}= \frac{(4(1+y^2))}{(4+x^2 )}

Q No. 21 Differentiate x^2 sec4x w.r.t involved variale

Q No. 22 Differentiate \tan^{3}{\theta} \sec^{2}{\theta} w.r.t involved variale

Q No. 23 Find \(\frac{dy}{dx}\) if y =xcosx

Q No. 24 Find \(\frac{dy}{dx}\) if x =ysiny

Q No.25 Differentiate sinx w.r.t cosx

Q No.26 If tany(1+tanx)=1-tanx, show that \frac{dy}{dx}=1

Q No.27 If y\sqrt{(tanx+\sqrt{(tanx+\sqrt{tanx) ) +… }}}\inftyProve that (2y-1)\frac{dy}{dx}=sec^2⁡x

Q No.28 Differentiate cot^{-1}⁡{\frac{x}{a}} w.r.t x

Q No.29 Differentiate \frac{1}{a}sin^{-1}⁡{\frac{a}{x}} w.r.t x

Q No.30 If y=tan⁡(ptan^{-1}{ x}), Show that (1+x^2 )y_{1}-p(1+y^2 )=0

Q No.31 Differentiate y = a^x w.r.t x

Q No.32 Differentiate (\ln{x})^x w.r.t x

Q No.33 Find f '(x) if f(x)=x^3 e^\frac{1}{x}

Q No.34 Find f '(x) if f(x)=e^{x}(1+ln{x})

Q No.35 Find f '(x) if f(x)=ln{x}(e^x +e^{-x})

Q No.36 Find f '(x) if f(x)=ln\sqrt{e^{2x}+e^{-2x}}

Q No. 37 Find \frac{dy}{dx} if y =x\sqrt{ln{x}}

Q No. 38 Find \frac{dy}{dx} if y = \frac{x}{ln{x}}

Q No. 39 Find \frac{dy}{dx} if y = ln⁡(9-x^2 )

Q No. 40 Find \frac{dy}{dx} if y = e^{-2x} sin2x

Q No. 41 Find \frac{dy}{dx} if y = xe^{sinx}

Q No. 42 Find \frac{dy}{dx} if y = 5e^{3x-4}

Q No. 43 Find \frac{dy}{dx} if y = (x+1)^x

Q No. 44 Find \frac{dy}{dx} if y = tanh^{-1}⁡(sinx)

Q No. 45 Find \frac{dy}{dx} if y = \sqrt{x} +\frac{1}{\sqrt{x}}

Q No. 46 Find y_{2} if x^2+y^2=a^2

Q No. 47 Find y_{2} if x=at^2 ,y=bt^4

Q No.48 Apply Maclaurin series to prove e^x=1+x+\frac{x^2}{2!} + \frac{x^3}{3!} + …

Q No.49 Define increasing and decreasing function

Q No.50 Define Point of inflection

Q No.51 Define Stationary point and critical point

Q No.52 Find extreme value for f(x)=1-x^2

Q No.53 Find extreme value for f(x)= 3x^2

Q No.54 Find extreme value for f(x) =5 + 3x - x^3

Q No.55 Find extreme value for f(x) =x^2-x-2

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Solutions of these all importan questions

Important short questions for Chapter 03 click here