5. Determine if the functions below are indeterminant forms and if so, what indeterminant form are...
Determine if the following limits have an indeterminant form, state it, and use L'Hopital's rule to compute the limit if possible. (a) limz-x++3x2–1 1 -3 (d) lim240 32° +sin(e"), (b) lime- 2 sin(3x) (e) lime-o(1 – x) tan(7), x2 – In(2/x) (f) limo+(1+2).. X-2 5.0 (c) lime+o022 –52
Quadratic forms arise often in geometry, physics and engineering and it is desirable to reduce these to canonical (standard) forms. Reduce the quadratic form:Q = 3x12 + 5 x22 + 3x32 - 2x2 x3 + 2x1 x3 - 2 x1 x2 to a standard form by making an approximate change in variables X = MY , where M is an orthogonal matrix. i) Write Q as X T AX . ii) Find the Eigenvalues of A. Is the quadratic form...
(1 point) Find lim vx+10. If the limit increases or decreases without bound, write inf or -inf, respectively. If it does not exist and cannot be represented by +oo or -oo, enter DNE. i.) If the limit does not exist, explain why. Check ALL that apply: A. The function is not defined beyond a particular bound in the direction of-co B. The function's behavior as x increases/decreases without bound does not approach one set value (for example, if the function...
Problem 2. (12 pts) The graph of a function fis given below. Answer the questions that follow. 110 6 2- 5 -6- - X-2 (i) (6 pts) Find the following limits. If a limit is infinite or does not exist, specify so. (Ipt each) a) lim f(x) = b) lim f(x)= c) limf(x) = d) lim f(x) = e) lim f(x) = g) limf(x) = (2 pts) Does f have any asymptote(s)? If yes, what kind? Write their equations. (iii)...
Does a precipitate form when the following solutions are mixed? If yes what is the empirical formula of the precipitate? 1) zinc sulfate & sodium sulfide 2) zinc acetate & manganese (II) chloride 3) iron (III) bromide & potassium hydroxide
Question 1. Consider these real-valued functions of two variables f(x, y) (a) (i) What is the maximal domain, D, for the functions f and g? Write D in set notation (ii) What is the range of f and g? Is either function onto? (iii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: 20-0, 20-2, 20-4 (Note: Use set notation, and draw a single contour diagram.) (v) Without finding Vg, on your...
Question # 2 [21 marks] a) Express z (-16-9i)° in the form a+bi where a,bER 1-i find Inz in polar form, zeC. b) Given z -3e c) (i) State the precise definition of the limit. (ii) A machinist is reguired to manufacture a circular metal disk witharea 1000cm (a) What radius produces such a disk? (b) If the machinist is allowed an error tolerance of +5cm in the area of the disk, how close to the ideal radius in part...
Question 1. Consider these real-valued functions of two variables TVIn (r2y2) f (x, y)- 9(r,)2 2+4 (a) (i) What is the maximal domain, D, for the functions f and g? Write D in set notation (ii) What is the range of f and g? Is either function onto? iii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: z0 0, 20 2, 204 (Note: Use set notation, and draw a single contour...
Question 1. Consider these real-valued functions of two variables: (a) i) What is the maximal domain, D, for the functions f and g Write D in set notation (ii) What is the range of f and g? Is either function onto? ii) Show that f is not one-to-one iv) Find and sketch the level sets of g with heights: zo- 0, 0 2, 20 4 Note: Use set notation, and draw a single contour diagram.) v) Without finding Vg, on...
(1 pt) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If either test can be applied to the series, enter CONV if it converges or DIV If it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA...