In Problems 1–18 use Definition 7.1.1 to find
5.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- plas). 4 3x Find the function with the derivative f' (x) = e * whose graph passes through the point P|0, 3arrow_forwardSet f(x) = In(9x - 8). Question 1 For k > 1, f (k) (1) =arrow_forwardThe questions in 1-5 are concerned with functions of two variables.1. Let f(x, y) = x2y + 1. Find(a) f(2, 1)(b) f(1, 3)(c) f(3a, a)(d) f(ab, a ab)(e) f(0, 0)2. Let g(x) = x sin x. Find(a) g(x/y)(b) g(xy)(c) g(x xy)3. Find g(u(x, y), v(x, y)) if g(x, y) = y sin(x2y), u(x, y) = x2y3, and v(x, y) =πxy4. Find F(g(x), h(y)) if F(x, y) = xexy, g(x) = x3, and h(y) = 3y + 1.5. Let g(x, y) = ye3x, x(t) = ln(t2 + 1), and y(t) = √t. Find g(x(t), y(t)).6. Suppose that the concentration C in mg/L of medication in a patient’sbloodstream is modeled by the function C(x, t) = 0.2x(e0.2teet), wherex is the dosage of the medication in mg and t is the number of hours sincethe beginning of administration of the medication.(a) Estimate the value of C(25, 3) to two decimal places. Include appropriate units and interpret your answer in a physical context.(b) If the dosage is 100 mg, give a formula for the concentration as afunction of time t.(c) Give a formula that describes the concentration after 1 hour in…arrow_forward
- 2. The number of hours of daylight in the SMH Lower Forum in month t of the year (with t = 0 being January) is given by the following function. d(t) = 3 sin (t – 2) + 12 a) Determine the number of hours of daylight in August. b) Identify the minimum number of hours of daylight and when it occurs.arrow_forwardH.W.4: Find f(3) (4) if fw) = /xarrow_forward1.Given f(x) = and g(x) = 16x* + 8x +1, h(1) = VE. a) Write the function f (h(9(*)). (9(f(x)). b) Write the function h 2. Given the function f(x) = sinx and g(x) = x², find the value of g(fe 3. Let f(x) = 1.2² and g(x) = 0.92. Identify the region for which f(x) > g(x)| 4. f(x) = log; x and g(x) = Vx- 4. What is the domain of f(g(x))and g(f(x):arrow_forward
- . If f(x) = 3x find the image and preimage of 6.arrow_forward2.2 Based on the Fundamental Theorem of Calculus, show in two statements what may be wrong with the following calculation: 3. 1 1 = - 3 4 z dx -1 -1 3arrow_forward1. Sketch a So when X 3 and f(x)>0 when quartic function for y = f(x) such that -4arrow_forwardarrow_back_iosarrow_forward_ios
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