10 1. Suppose f(x) and g(x) are differentiable at x = 0 and f'(x) and 9' () are continuous at r = 0. If f(0) = g(0) = 0,

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10 1 Suppose F X And G X Are Differentiable At X 0 And F X And 9 Are Continuous At R 0 If F 0 G 0 0 1 (59.96 KiB) Viewed 18 times

10 1 Suppose F X And G X Are Differentiable At X 0 And F X And 9 Are Continuous At R 0 If F 0 G 0 0 2 (65.76 KiB) Viewed 18 times

Can you please do questions 1-6. The top graph is for #3 while the bottom graph is for #4.
Thank you very much for your help.
10 1. Suppose f(x) and g(x) are differentiable at x = 0 and f'(x) and 9' () are continuous at r = 0. If f(0) = g(0) = 0, $'(0) = 5 and 9'(0) = -3, evaluate the limit f (tan-'(x)) lim g (sin(x)) 2. Evaluate the following limits: tan-1 (Inc)) (a) lim 3.2-3 (b) lim in (r)(e-2-1) 20+ y = f(x) y = g(3) 3. Use the graph shown to evaluate lim f(3) 20 9(2) 21 YE y=-4.1 +4 y=2.5. - 2.5 4. Use the graph shown to evaluate lim f(x) 2+1 g(x) y = g() y = f(x) 5 - 3 5. Use an appropriate substitution to rewrite each integral given below in a "simpler" form, but do not evaluate the integral. e 3x + 1 day (a) ſem fse (b) (2+1) f(x + In(:)) de 6. Evaluate the indefinite integrals given below. In(a) sin(Inºx)) dar 23 (a) / (b) 1+eva A+ dac

4 3 y = f(x2) 2 y = g(x) -5 -4 -3 -2 3 4 5 6 7 Y = -X -2 y = x -3 6 y = -4x + 4 1 4 y = 2.5x – 2.5 3 2 y = g(x) 1 y = f(x) -5 -4 3 -2 0 2 3 4 5 6 -1 -2