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.)
BIHAR CET Limits and Continuity — practice questions — page 2
Explore 131 free Limits and Continuity questions in BIHAR CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Limits and Continuity with Quill →Limits and Continuity questions and exercises with answers
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.
How to practise
- Choose a Limits and Continuity question and try to work out your answer.
- Open the question to check the correct answer and read its worked solution.
- Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.