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IGNOU BDP MTE 1 2024 Solution

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Last Date of Submission of IGNOU MTE-01 (BDP) 2024 Assignment is for January 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).
Semester Wise
January 2024 Session: 30th March, 2024 (for June 2024 Term End Exam).
July 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).

Title Name	ignou MTE 1 solved assignment 2024
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	BACHELOR DEGREE PROGRAMMES
Course Code	BDP
Course Name	Bachelor Degree Programmes
Subject Code	MTE 1
Subject Name	Calculus
Year	2024
Session	-
Language	English Medium
Assignment Code	MTE-01/Assignmentt-1//2024
Product Description	Assignment of BDP (Bachelor Degree Programmes) 2024. Latest MTE 01 2024 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU MTE-01 (BDP) 2024 Assignment is for January 2024 Session: 30th September, 2024 (for December 2024 Term End Exam). Semester Wise January 2024 Session: 30th March, 2024 (for June 2024 Term End Exam). July 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).
Assignment Code	MTE 1/2024

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Questions Included in this Help Book

Ques 1.

The function f, defined by )x(f = cos x + sin ,x is an odd function.

Ques 2.

$\frac{\mathrm{d} }{\mathrm{d} x}\left [ \int_{2}^{e^{x}}ln\, t\,dt \right ]=x-ln\,2.$

Ques 3.

The function f, defined by $f(x)=\left | x-2 \right |,$ is differentiable in [0,1].

Ques 4.

$y=x^{2}-3x^{3}$ has no points of inflection.

Ques 5.

$y=-x^{2}$ is increasing in [− 5, − 3] .

Ques 6.

Find $\frac{\mathrm{d} y}{\mathrm{d} x},$ if $y=xsin^{-1}\,x+\sqrt{1-x^{2}}.$

Ques 7.

Evaluate $\int_{0}^{\pi}\frac{x\,sin\,x}{1+cos^{2}\,x}dx.$

Ques 8.

Find $\lim_{x\rightarrow1}\frac{x^{3}-3x+2}{x^{2}-5x+4}.$

Ques 9.

Trace the curve $y^{2}=x^{2}(x+1)$ by the stating all the properties used to trace it.

Ques 10.

Find the length of the curve given by $x=t^{2}\,,y=2t^{2}\,in\,0\leq t\leq 2.$

Ques 11.

Find the angle between the curves $y^{2}=ax\,and\,ay^{2}=x^{2}(a>0),$ at the points of intersection other than the origin.

Ques 12.

Evaluate $\int \frac{x^{2}dx}{(x-3)(x-5)(x-7)}$

Ques 13.

Use Simpson’s method to approximate $\int_0^{8}(x^{2}-x+3)dx$ with8 sub-intervals.

Ques 14.

Find the derivatives of $ln(1+x^{2})w.r.t.\,\,tan^{-1}\,x.$

Ques 15.

The curve $ay^{2}=x(x=a)^{2}\,,a>0$ has a loop between x = 0 and x = a. Find the area of this loop.

Ques 16.

Obtain the largest possible domain, and corresponding range, of the function f , defined by $f(x)=\frac{x-2}{3-x}.$

Ques 17.

Expand $e^{2x}$ in powers of $(x-1),$ up to four terms.

Ques 18.

Verify Rolle’s theorem for the function f , defined by $f(x)=x(x-2)e^{-x},$ on the interval $[0,2].$ .

Ques 19.

Is the function f , defined by

$f(x)=\frac{x^{2}-5x+4}{x^{2}-16},x\neq 4$

$f(4)=0,$ continuous at $x=4?$ Give reasons for your answer.

Ques 20.

Evaluate $\int_{0}^{1}x^{2}e^{3}dx.$

Ques 21.

Using Trapezoidal rule, calculate $\int_{0}^{1}\frac{dx}{1+x^{2}}$ by dividing the interval [0,1] equal subintervals. Hence evaluate π.

Ques 22.

Find $\frac{\mathrm{d} y}{\mathrm{d} x},if\,y=x^{sin\,x}+(sin\,x)^{x}$

Ques 23.

Find the perimeter of the cardioid $r=a(1-cos\theta ).$

Ques 24.

If the first three non-zero terms of Maclaurin’s series for sin x are used to approximate sinπ ,2/ show that the error is less than 1/50.

Ques 25.

Find the least value of $a^{2}sec^{2}\,x+b^{2}\,cosec^{2}x,$ where $a>0,b>0.$

Ques 26.

Evaluate $\lim_{x\rightarrow 0}(1+x)^{1/x}$

Ques 27.

Find the slope of the normal to the curve $y=x^{3}\,at\,\left ( \frac{1}{2},\frac{1}{8} \right ).$

Ques 28.

Find the points of inflexion of the curve $y=\frac{a^{2}x}{x^{2}+a^{2}}.$ Also, show that they lie on a straight line.

Ques 29.

Evaluate $\int e^{x}\,.\frac{x^{2}-x+1}{(1+x^{2})^{3/2}}\,dx$

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