Solved: Sketch the graphs $y = \left( \sin(x + 1) \right)^3 + \ln(x + 2)$ and $y = 2 +... [IB Mathematics Analysis and Approaches (AA)]

Question

HLPaper 2

Sketch the graphs $y = \left( \sin(x + 1) \right)^3 + \ln(x + 2)$ and $y = 2 + \cos(x + 1)$ for 0 < $x$ ≤ 9.

[2]

Verified

Solution

A1A1 Note: Award A1 for each correct curve, showing all local max & mins. Note: AwardA0A0 for the curves drawn in degrees. [2 marks]

Hence solve ${\sin}^3 x + {\ln} x - {\cos} x - 1 < 0$ in the range 0 < ${x}$ ≤ 9.

[4]

Verified

Solution

$x$ = 1.35, 4.35, 6.64 (M1)

Note: Award M1 for attempt to find points of intersections between two curves.

0< $x$ < 1.35 A1 Note: Accept $x$ < 1.35.

4.35< $x$ <6.64 A1A1 Note: Award A1 for correct endpoints, A1 for correct inequalities.

[4 marks]

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