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In Problems 12–16, for the given limit
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Calculus: Single And Multivariable
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- 2. Evaluate lim,. 3. Find the domain of the function g(x) = v1- x In x . 4. Find f'(x), if f(x) = (2x – 8x²)-²(3x + 1).arrow_forward4. Given that f(x)= 4x² –3 ,xarrow_forward16. If f(x) = 2x – 1, what is lim (x+h)-f(x), x-h h B.- С. — 2 D. 2 NINarrow_forwardB. The graph of f(x) is given in Figure 5. Determine the following limits: 1. lim f(x) 4. lim f (x) x→-4 x-3 2. lim f(x) 5. lim f(x) x--1 x→5 3. lim f(x) x→1 (-1,4) (1,4) (÷1,-2) (5,-2). (3,-4) (4, 5) Figure 5arrow_forward3. Let f(x) = c.(x-4)+2 if 0 ≤x≤4 if x > 4 where c denotes a real constant. (a) Show that lim f(x) = lim f (x) and that fe is continuous at x = 4 for any real c. x->4+ X-4 (b) Sketch the curves y = f(x) on separate graphs for c=0, c=1, and c= -1. (c) Determine the unique value of c for which fe is differentiable at x = 4, i.e., find c so that (f)+ (4) = (f)'_ (4).arrow_forwardSuppose we know the following information about the function f (x): f(-1) = -4, f (2.5) = 3, f(T) = 2.4 and f (1) does not exist lim,-1- f (x) = -4 lim, y→-1* ƒ (x) = -4 lim, 2.5+ f (x) = -0 lim,n f (x) = 0 lim,8- f (x) = 3 lim,8* f (x) = 3.01 What does this information tell us about the continuity of f (x) ? At a = -1, f (x) is/has a [ Select] At r = 1, f (x) is/has a [Select] At r = 2.5, f (x) is/has a [ Select] At x = T, f (x) is/has a [ Select ] At r = 8, f (x) is/has a [Select] [ Select ] jump discontinuity infinite discontinuity there is not enough information to tell anything discontinuous, but there is not enough information to tell which type removable discontinuity continuous Ouestion 5arrow_forwardarrow_back_iosarrow_forward_ios
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