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Ohio University, Main Campus Math 2301 Spring 2025 Time Trial 2 Cody Hupp 2301 (solved)
Typology: Exams
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Problem 1: Differentiate the following functions (DO NOT SIMPLIFY YOUR ANSWER): a. y=e:u'_17^2
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?r}() > T‘ (4= )4 (lal4)e2) (44°- o1) sin(2x)
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@ (^) f is continuous (^) at x = (^) 4. /s v b f(d)=
d. The slope of the tangent line of f at x = 3is 2.
x243x =
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Problem (^) 5: VBFind ax USIng implicit (^) differentiation (^) of the following (^) relation. x? = 2xy + 3y = ZX~2 (^) Y - (^) 2’(/&{(O/y 7 é‘)‘fl", ) dy ;,T; (‘?K-¢ (,/> - ‘7Y’?/ 4 (“2)("/6/) Problem 6: In this Question, distance is measured in fe (^) et (ft) and time is measured in seconds (s). Provide correct units (^) in your (^) answers. a. Ifaparticle has the velocity function v(t) =3t — 2, < t < 3:
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ii. Find the displacement traveled by the particle.
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(B1)-1)-1g 27 (27 85 / i 2 b. At what time (^) will an object by at rest (^) if its position function (^) is given by p(t) (^) = ¢3 2 6t% + 9t + (^) 4? 2 % PG) 7 3 -4 44 3¢ 5 gl ‘7('(1’:7‘(43) (t-2)(4-))
Problem 7: a. Find (^) the equation of the tangent (^) line to the graph at the given (^) x-value, f(x):xZTl, x=3 ///6_:—’(_'_1(___2_2. A XA (//fl
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Problem 8: Let x and y be two numbers satisfying 2x + 3y = 60. What values of x and Y maximize the product xy? Zx 42z ko ?(azgéotéy)v z Zy: 60'; Peoz GOy, _z v = (^) 60-3 (^) Loy—————— (^) s0y- (^) % y°
) q^ shaded Problem 10: Use the graph of f(x) to find the values of the following {ntef‘rals.nT::?e ;‘ umber of (^59) square in the units; 12 ; the
second Y^ ‘^ rea^ of^21 squar shaded (^) region (^) has an area (^) of (^11) square (^) units; and the (^) third shaded (^) region (^) has (^) an a y el (^50 )
3 ¢ (^) L (^) Fx)dx (^) = 32 44 0 3 -~ (^35) L o= e) The average value of the function: 4/3 o Problem 11: A5 ftladder is leaning against a wall. The top of the ladder slides down a vertical wall at? rate of 2 ft/s. At what rate is the bottom of the ladder moving away from the wall when the top of the ladder is 3 ft off the ground? 2l = £49:28 (^) xz*/7f
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