IGNOU MTM MTM 7 Managing Sales and Promotion in Tourism Solved Assignment ENGLISH

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MTM 2025 - ENGLISH

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MTM 7: Managing Sales and Promotion in Tourism

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Title Name	IGNOU MTM MTM 7 Managing Sales and Promotion in Tourism Solved Assignment ENGLISH
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
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
Format	Ready-to-Print PDF (.soft copy)

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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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Course: Master of Arts in Tourism Management (MTM)
Subject: MTM 7 - Managing Sales and Promotion in Tourism
Session: January 2025 - December 2025
Language: ENGLISH

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Product Information

Course Name	Master of Arts in Tourism Management
Course Code	MTM
Subject Code	MTM 7
Subject	Managing Sales and Promotion in Tourism
Programme	MASTER DEGREE PROGRAMMES Courses
Language	ENGLISH
Material Type	Solved Assignment – Soft Copy / PDF

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