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C6129B4C-6B97-4A53-93F7-82A97FAB4AE5.png - .8 9 24 Given...

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Unformatted text preview: .8 9 24) Given the following graph of function, g(x), 3 3 PM 53% a) Find all x values where the graph is discontinuous. b) For each discontinuous x value, name the type of discontinuity. c) For each discontinuous x value, state why it fails the formal definition of continuity. d) Determine the intervals where the function is continuous. 6 of 7 a) X= -4, -3, -2 34 d(-co,-4) 5) point / loritovablo -> x=-4, 4 (-4,-3)v (Infink -X=-3 3 (-3-25V Jump->x=-2 (-2, 3)V i ) Ha) DUE-,X--4 iu ta tami (3, 4) 0 udi) LIMA DUE +X--3, -2,3 x=4 (4, 00) 6 25) Given: y = x2 - 5x + 9, find >. Show all work using the formal definition of the derivative. he= lim f(kin ) -To> h->0 -lim (x4h)?-s(xth) +q - (xisx +9) h-70 u um x taxt the sy-sita-242x A_Jim ax th -5 h-0 h -ax-S 26) a) What is the equation of the tangent line at x = -3 for the function f (x) = 5x2 - 2x - 2? $' (x )- 10x-a y=$ (-3)= 51-3) -2(-3) - m= $'(-3) = 10(-3)-2= -38 =49 y-49- -3a(x+3) b) What is the slope of the normal line for f(x)? 1 slope 3a 27) The graph of f (x) is shown to the right. a) Is f continuous at x = 0? Why or why not? no, lim fu) + limf() X -, 0 X-70* b) Is f differentiable at x = 0? Why or why not? no, be cause it isn't Continuous c) Using the domain of [-3, 3], state the x-intervals where f(x) is differentiable (-3, 0Ju(D, 3) 7 28) Find the derivative of the following functions. State the formula used for each. us Rodud lol a) 3 = (x3 - 6x) (2 - 4x3) Quohert )y - 23+3 u'.v-u'v u'.v+u.V u= 3x2V V=-lax N's 8x v'= 3x2 va Sx 4+24 x - 12x 4 ,-(8M(x 343)-(4x) (3x?)...
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Christopher Reinemann
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