alleryStart learning →cos(90°) equals:
- 1
- ∞
- 1/2
- 0
Show answer and solution
Correct answer: D. 0
cos(90°) = 0. (cos(0°) = 1, cos(180°) = -1.)
CG PET Limits and Continuity — practice questions — page 2
Explore 131 free Limits and Continuity questions in CG PET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–60 of 131.
cos(90°) equals:Read the answer and worked solution →sin²θ + cos²θ equals:Read the answer and worked solution →tan(45°) equals:Read the answer and worked solution →In which quadrant is sin θ positive and cos θ negative?Read the answer and worked solution →lim_(x→2) (x² - 4)/(x - 2) =Read the answer and worked solution →lim_(x→0) sin(x)/x =Read the answer and worked solution →For limit to EXIST at x = a, left-hand and right-hand limits must:Read the answer and worked solution →A function f is continuous at x = a if:Read the answer and worked solution →d/dx (xⁿ) = ?Read the answer and worked solution →lim_(x→0) (1 - cos x)/x² =Read the answer and worked solution →lim_(x→∞) (1 + 1/x)^x =Read the answer and worked solution →lim_(x→0) (e^x - 1)/x =Read the answer and worked solution →lim_(x→0) (sin 3x)/(sin 5x) =Read the answer and worked solution →d/dx (sin x) =Read the answer and worked solution →d/dx (eˣ) =Read the answer and worked solution →d/dx (ln x) =Read the answer and worked solution →Find d/dx (x² sin x) by product rule:Read the answer and worked solution →By chain rule, d/dx [sin(x²)] =Read the answer and worked solution →lim_(x→∞) (3x² - 5)/(7x² + 2) =Read the answer and worked solution →l'Hôpital's rule applies to limits of form:Read the answer and worked solution →Find dy/dx by implicit differentiation for x² + y² = 25:Read the answer and worked solution →d/dx (xˣ) where x > 0:Read the answer and worked solution →For f(x) = sin(1/x) for x ≠ 0, what is the limit as x → 0?Read the answer and worked solution →Differentiation by chain rule for d/dx [ln(sin x)]:Read the answer and worked solution →lim_(x→0) [(1 + x)^(1/x)] =Read the answer and worked solution →Higher-order derivative: d²/dx² (x⁴) =Read the answer and worked solution →f(x) is discontinuous at x = a if which condition fails?Read the answer and worked solution →For y = x³ - 6x² + 9x, find critical points (where y' = 0):Read the answer and worked solution →By Taylor expansion around x = 0: e^x = 1 + x + ___:Read the answer and worked solution →What does the sign of f ′(x) tell you?Read the answer and worked solution →
Worked practice questions
sin²θ + cos²θ equals:
- cos 2θ
- 2
- 0
- 1
Show answer and solution
Correct answer: D. 1
**Pythagorean identity:** sin²θ + cos²θ = 1 for all θ.
From right triangle x² + y² = r².
Sin = y/r, cos = x/r, so sin² + cos² = (x²+y²)/r² = 1.
tan(45°) equals:
- ∞
- 0
- 1
- √3
Show answer and solution
Correct answer: C. 1
We have tan(45°) = sin(45°)/cos(45°).
That is tan(45°) = (1/√2)/(1/√2).
So tan(45°) = 1.
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