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1. It is known that has a Fversion of the test. Find the limt lim (Vx+&+1...
Find the limit lim (V2x2 + 4x +1 – V2x2 + x - 1). Show 300 your work in the PDF version of the test.
find the limits analytically, show all steps
x²–8 1. lim *+2 X-2 2. lim x3 Vx+1-2 x-3 1 3. lim 3+ x 3 x2 - 2x -15 4. lim *+-3 x2 + 4x +3 x0 X (4+ x)-16 5. lim X>0 x² - 4 6. lim 1+2 r -8 x x+sin x 7. lim 10 X sin²x 8. lim :-) x 3 sin(4x) 9. lim *** sin(3x) r? 10. lim 1981-COSI 1 11. lim x → X-1 = 1 12....
A function f is a ratio of quadratic functions and has a vertical asymptote x = 3 and just one x-intercept, x = 1. It is known that f has a removable discontinuity at x = -1 and lim f (x) = 5. 27-1 Evaluate lim f (x). Show your work in the PDF 200 version of the test.
5. Find the e-coordinate of the point on the curve : +3y3 = 3ay where the tangent is horizontal. Show your work in the PDF version of the test. 7. How many real roots does the equation ! 9x +c=0 have in the interval (-3,0? Hint: use the Mean Value Theorem (Rolle's Theorem). Show your work in the PDF version of the test. A. At most two real roots B. At least one real roots C. No real roots D....
5a) (5 pts) Find lim inf (xn) and lim sup (rn), for rn = 4 + (-1)" (1 - 2). Justify your answer 5b) (5 pts) Find a sequence r, with lim sup (xn) = 3 and lim inf (x,) = -2. 5c) (10 pts) Let {x,} be a bounded sequence of real numbers with lim inf (x,) = x and lim sup (x,) = y where , yER. Show that {xn} has subsequences {an} and {bn}, such that an...
) Page 2 ot B Test 3 Version A Test 3 Version A Page 3 of 8 Problems (20 Points each) Show your work for full credit 1. A force R-(+3j)N is applied to a 10 kg block. The block slides on a horizontal frictionless floor from an initial position of (-5 i +6f)m to a final position of (o1 10]) m. work done by the applied force. Find the
9. Find the absolute maximum value of the function (1) = 2/32 - sin(4x) on the interval (0, 8/12). Show your work in the PDF version of the test.
Suppose f is a function that satisfies the equation f (x + y) = f (x) + f(y) + xºy + xy2 + xyz + xy for all real numbers x and y. Suppose also that f(x) lim = -1. Find f' (a). Show your work in 30 the PDF version of the test. 2
Use Part 1 of the Fundamental Theorem of Calculus 33 to find the derivative of g(x) = ſ et dt. Show your In x work in the PDF version of the test. e* dt. Show your
3. Suppose f is a function that satisfies the equation f (x + y) = f () + f (y) +2°y +zy+ xy + xy for all real numbers x and y. Suppose also that limma) = -1. Find f' (r). Show your work in the PDF version of the test. 20 Copyright 2020 Victor Padron