Concept explainers
In Problems 37‒40 proceed as in Example 6 to solve the given initial-value problem. Use a graphing utility to graph the continuous function y(x).
40.
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Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th
- If F(x) = f(g(x)), f(2) = 8, f'(2) = 4, g(5) = 2 and g' (5) = –2, then F' (5) is %3D %3D %3D %3D 16 -8 12 32arrow_forwardIn Problems 39–46, show that 1f ∘ g2 1x2 = 1g ∘ f2 1x2 = x.arrow_forwardSuppose that h(x) = f(g(x)), and that we have the following in- formation about these functions: f(3) 2 g(3) = -1 f'(3) = 4 g'(3) = 6 f(-1)%3D7/5 f'(-1) 33/2 g'(-1) = 0 g(-1) = 2/3 f(6) = 1/3 g(6) = 3 f'(6) = 4 g'(6) = 10 What's the value of h'(3)? a) 6 b) 9 novoarrow_forward
- Suppose f, f', g, and g' have the following values: 1 2 3 4 f(x) 8 2 1 -8 f'(x) g(x) 10 -7 - 2 6 -6 – 253 - 252 - 246 - 248 - 262 - 64 56 14 - 15 23 (2),6 At the half-time show for a Milwaukee College football game, a balloon will travel along a path with equation z + y = f(x)g(x) and will be released at the point where x = 2. To ensure the safety of the crowd, Sophia needs the equation of the line tangent to the graph of 2° + y° = f(x)g(x) at x = 2 For this question, if you choose to use decimals, be sure that you round your numbers to at least 4 decimal places. The equation of the tangent line is:arrow_forwardfind the interverse of the fuction f (x)= 2x + 3/x-4arrow_forwardLet g(x) = f(t) dt, where f is the function whose graph is shown. Assume g(-3) = 0. %3D %3D -3 Compute each of the following: Show computations!! A. Graph of f (i) g(-2) 4 (ii) g(0) -5 -4 -3 -2 2 3. (ii) g(2) -2 3- -4 (iv) g(5) В. On what interval(s) is g (i) increasing (ii) concave up (ii) decreasing (iv) concave down С. At what values of x on the interval [-3, 5] does g have (i) An absolute maximum Graph of g (ii) An absolute minimum (ii) Any inflection points -5 -4 -3 -2 -14 2. 3. 4. 5 6 -2 -3- D. Sketch a graph of g on [-3,5]. Use the grid > -4 -5 %24arrow_forward
- 11. Suppose that for a function f, the equation f (x) = 0 has no real-number solutions. Which of the following statements MUST be true? 1. f(x)> 0 for all x in the domain of f. 2. f has no y-intercepts. 3. f has no x-intercepts. 4. fis an invertible function.arrow_forwardFind a linear approximation to the following function at the point x = 1 y = f(x) = x5 - 4x² + 4x³ - 12x² + 21x6 Select one: a. y = 5-3(x - 1) b. None of these c. y = 42(x - 1) d. y = 5-2(x - 1) e. y = 4 − 3(x − 1) O O O O |||arrow_forwardDo problems 3, 5, 8, 10, 14, 17, 25, 29, 31, 37, 40.arrow_forward
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