(x² + 1 if x <-1 g(x) = }2 if x = -1 (6– x if x > -1

Q: 1. Find the function y(t) satisfying y' = ev-t(1+t?) sec y with y(0) = 0.

A: Claim: solution for with y(0)=0. Integrating both sides we get, Take u=e-y then du=-e-y  and…

Q: Check the function y=x²+1 whether have a symmetry about x or y axis

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Q: A car's movement is represented by the function 2x3 + 6x2 + 2x + 3 in kilometers reco at an hourly…

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Q: The function f1x2 = x2 is decreasing on the interval

A: fx=x2 Differentiating with respect to x, we get f'x=2x

Q: Questiun 4 At which interval is the function decreasing? 10 10 O (7,22) O (7,9) O (0,3) O (9,22)

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Q: Find the open intervals where the function f(x)=-2/x+1 is concave up and concave down. State any…

A: According to the given information, it is required to calculate the interval where the function is…

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: Express the rule "Subtract 11, then square" as the function f(x) = I.

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Q: Find the inflection points for the function f(x) = 2x6 + 3x5 – 10x*. -

A: Note :- Inflexian points of a function can be calculate by putting f"(x) =0 and solve for x.  We get…

Q: Give an example of a real function that is increasing on the interval (0,2), and decreasing on (2,…

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Q: Show whether the function y=x² is considered as even or odd function

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Q: Choose the interval where the function is positive. -4 -6 -2 2 2 4 -6 -00 < < 00 0<< 00 C -2 <<2 -00…

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Q: Determine which pair of points can represent as the absolute extrema of the given function at the…

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Q: Plot the functions x, x2, exp(-x), exp(-x2) on a single graph for x between 0 and 5. Repeat the…

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Q: Find the value k that makes the function continuous. kx f (x) = x > 9 - -7x – 7, x < 9

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Q: Choose 1 answer: A -4<x < -3 B) -1< a < 0 4 < a < 5

A: For F(x) is positive where f'(x)&gt;0 so the slope of the curve is positive

Q: Find the point on the line y = −3x + 4 closest to the point (-9, -10). A function s(x) giving the…

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Q: 7+6z – zº x 4 тх + b,

A: Given that,    A function is continuous everywhere means the function is continuous at every point…