IGNOU MTM 7 SOLVED ASSIGNMENT

MTM 7: Managing Sales and Promotion in Tourism

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Title Name	IGNOU MTM 7 SOLVED ASSIGNMENT
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	MASTER DEGREE PROGRAMMES
Course Code	MTM
Course Name	Master of Arts in Tourism Management
Subject Code	MTM 7
Subject Name	Managing Sales and Promotion in Tourism
Year	2025
Session	-
Language	English Medium
Assignment Code	MTM 7/Assignment-1/2025
Product Description	Assignment of MTM (Master of Arts in Tourism Management) 2025. Latest MTM 07 2025 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU BEGC-131 (BAG) 2025-26 Assignment is for January 2026 Session: 30th September, 2026 (for December 2025 Term End Exam). Semester Wise January 2025 Session: 30th March, 2026 (for June 2026 Term End Exam). July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).
Format	Ready-to-Print PDF (.soft copy)

📅 Important Submission Dates

January 2025 Session: 30th September, 2025
July 2025 Session: 30th April, 2025

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MTE 07 (January 2025 - July 2025) - ENGLISH

ASSIGNMENT

Course Code: MTE-07

Assignment Code: MTE-07/TMA/2025

Maximum Marks: 100

1. State whether the following statements are true or false. Give reasons for your answers.

(i) $lim_{x o 0}frac{x^2sin(frac{1}{x})}{sin x}=1$

(ii) A real-valued function of three variables which is continuous everywhere is differentiable.

(iii) The function $F:mathbb{R}^2 omathbb{R}^2, ext{defined by}F(x,y)=(y+2,x+y),$ is locally invertible at any $left(x,y ight)epsilon R^{2}$

(iv) $f:[-1,1] imes[-2,2] omathbb{R}, ext{defined by}$

$f(x,y)=egin{cases}x,& ext{if}y ext{is rational}\0,& ext{if}y ext{is not rational}end{cases}$ is integrable.

(v) The function $f:mathbb{R}^2 omathbb{R}, ext{defined by}f(x,y)=1-y^2+x^2,$ (.0,0)

2) (a) Find the following limits:

(i) $lim_{x o+infty}left(frac{x^2}{8x^2-3} ight)^{1/3}$

(ii) $lim_{x o 0^+}(sin x)^{sin x}$

(b) Find the third Taylor polynomial of the function $f(x,y)=1+5xy+3^2 y ext{at}(1,2).$

$f(x,y)=egin{cases}frac{x^2 y}{sqrt{x^2+y^2}},&(x,y) eq(0,0)\0,& ext{otherwise}end{cases}$

3) (a) Let the function f be defined by

$f(x,y)=egin{cases}frac{3x^2 y^4}{x^4+y^8},&(x,y) eq(0,0)\0,&(x,y)=(0,0)end{cases}$

Show that f has directional derivatives in all directions at.(0,0)

(b) $ext{Let}x=e^rcos heta,y=e^rsin heta ext{and}$ be a continuously differentiable function of x and y, whose partial derivatives are also continuously differentiable. Show that

$frac{partial^2 f}{partial r^2}+frac{partial^2 f}{partial heta^2}=(x^2+y^2)left(frac{partial^2 f}{partial x^2}+frac{partial^2 f}{partial y^2} ight)$

Find |2 b − a + 3c l.

4. (a) Find the centre of gravity of a thin sheet with density δ(x, y) = y, bounded by the

curves $y=4x^2 ext{and}x=4.$

(b) Find the mass of the solid bounded by $z=1 ext{and}z=x^2+y^2,$ the density function being δ (z,y,x )= .|x|

5. (a) State Green’s theorem, and apply it to evaluate

$oint_C(3x^2-4y),dx-(2x+y^3),dy,$

Where C is the ellipse $4x^2+9y^2=36.$

(b) Find the extreme values of the function

$f(x,y)=x^2+y ext{on the surface}x^2+2y^2=1.$

6. (a) State a necessary condition for the functional dependence of two differentiable functions f and g on an open subset D of . R²Verify this theorem for the functions f and g, defined by

$f(x,y)=frac{y-x}{y+x},quad g(x,y)=frac{x}{y}.$

(b) Using the Implicit Function Theorem, show that there exists a unique differentiable function g in a neighbourhood of 1 such that $g(1)=2 ext{and}F(g(y),y)=0.$ in a neighbourhood of (,1,2) where

$F(x,y)=x^5+y^5-16xy^3-1=0$

defines the function F. Also find g′( y).

(c) Check the local inevitability of the function f defined by $f(x,y)=(x^2-y^2,2xy)$ at ,(1 − .1) Find a domain for the function f in which f is invertible.

7. (a) Check the continuity and differentiability of the function at (0,0) where

$f(x,y)=egin{cases}frac{2x^3 y}{x^2+y^2},&(x,y) eq(0,0)\0,& ext{otherwise}end{cases}$

(b) Find the domain and range of the function f , defined by $f(x,y)=frac{2xy}{x^2+y^2}. ext{Also}$

find two level curves of this function. Give a rough sketch of them

8. (a) Evaluate $oint_C(2x^2+3y^2),dx,$ where C is the curve given by

$x(t)=at^2,quad y(t)=2at,quad 0leq tleq 1.$

(b) Use double integration of find the volume of the ellipsoid

$frac{x^2}{4}+frac{y^2}{9}+frac{z^2}{16}=1.$

9. (a) Find the values of a and b, if

$lim_{x o 0}frac{x(1+acos x)-bsin x}{x^3}=1$

(b) Suppose S and C are subsets of R³. S is the unit open sphere with centre at the origin and C is the open cube = ${P(x,y,z)mid-1<x<1,-1<y<1,-1<z<1}$

Which of the following is true. Justify your answer.

(i) S ⊂ C

(ii) C ⊂ S

(i) $sqrt{x^2+y^2}$

(ii) $sqrt{4-x^2-y^2}$

(iii) x-y

(iv) y/x

10. (a) Does the function

$f(x,y)=frac{x^2-y^2}{x^2+y^2},quad x eq 0,y eq 0$ satisfy the requirement of Schwarz's theorem at

(1,1)? Justify your answer.

(b) Locate and classify the stationary points of the following:

(i) $f(x,y)=4xy+x^4-y^4$

(ii) $f(x,y)=xy+frac{2}{x}+frac{4}{y},quad x>0,y>0$

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