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pls explain the answer clearly and writ the answer neatly................................................ Problem 6. Consider the following functions...
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Problem 10. It can be shown that if Xi, X2 and Y are sets, f : X1 → Y and g :X2→ Y are functions, and Xin X,-o, then f U g is a function X,U X2 → Y. 10(a) Give an example where X, X2 and Y are sets, f : X1 → Y and g : X2 → Y are functions and fug is not a function. 10(b)...
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ANS 2 (C)
ANS 3 (D)
Problems 1-6 refer to the area shown 6 cm 2 cm 4 cm 2 cm Problem 2 What are the z- and y-coordinates of the centroid of the perimeter line? (A) 1.0 cm; 3.8 cm (B) 1.0 cm; 4.0 cm (C) 3.0 cm; 3.7 cm (D) 3.0...
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A metric space is a set M together with a distance function p(x, y) "distance" between elements a and y of the set M. The distance function must satisfy that represents the (i) f (x,y) 0 and p(z, y)--0 if and only if x y; (ii) ρ(z,y)=ρ(y,x); (iii) ρ(z, y) ρ(z, z) + ρ(z, y) for all x,...
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3. Let f(x, y, ). g(y,z) and h(x,y,z) be C2 scalar functions. Prove the following identity: (a) By direct calculation (without using the vector identities) ( b) Using the vector identities. Clearly state which identities you have used .
3. Let f(x, y, ). g(y,z) and h(x,y,z) be C2 scalar functions. Prove the following identity: (a) By direct calculation (without using the vector identities) ( b) Using the vector identities. Clearly state...
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Problem 1) A semiconductor material is exposed to an electric field and non-uniform distribution of electrons and holes as shown. Determine the direction of carrier flow due to all possible mechanism and the associated currents for electrons and holes. Label your answer clearly. p(x) nge) rNo E (Electric Field)
MATH119 - Final tion 6 Let f and gbe differentiable functions on R and consider the function et answered h(z) = 5" }()g()dt ed out of 5 ag question Which of the following is equal to h'()? (Warning. Be careful that, in the definition of h(x) the definite integral is with respect to t.) Select one: a. f(2).9(3) A b. [*}"(w)g(t)dt + f(z)g(0) c. f'(x) · g(x) d. [ 7)g(e)dt + f(2)() eſ sz)ge)dx + $()() Next page
Problem 8. True or False (You do not need to explain your answer but must indicate clearly “T” or “F.” You will lose points in your T or F is not clearly indicated.) (a)_ Given z=f(x,y), fxy(x, y) is always equal to fxx (x, y). (b)_ Tangent plane to z= f(x, y) at (x,,y.) always approximates the value of z near (xo, y.). (c) __ If fx and f, exists, then z= f(x,y) is differentiable. (d) __If f{(1,2)=0, then fx,...
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Calculate the gradient of f(x, y) = sin(x2 – 4y) Vf = Calculate the gradient of h(x, y, z) = x-3y-22-2 Vh= Calculate the directional derivative of S(x,y) = xy in the direction of y = -1 + 2) at the point P = (1,2). Remember to normalize the direction vector. D.$(1.2) = 11 point Calculate the directional derivative of f(x,y) = cos (xy) in the...
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4. Consider the linear transformation T which transforms vectors ) by refection in the yaxis (a) Express the vector 코, = T(2), the result of the linear transformation T on a, in terms of the components r and y of i. (b) Find a matrix T such that T(F) = Ta, using matrix multiplication. (c)...