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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.
Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Directions : In the following questions, A statement of Assertion (A)...
Given y = 2cos2(3x)
dy/dx = 2 x 2 x cos(3x) x (- sin 3x) x 3
dy/dx = -6 sin 6x dx
∴ R is true.
Since the slope of tangent is zero, the tangent is parallel to the X-axis. That is the curve has a horizontal tangent at x = π/6. Hence A is false.
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Directions : In the following questions, A statement of Assertion (A)...
Assertion and Reasoning in Trigonometry
Explanation:
Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.
Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.
Explanation:
The given curve is y = 2cos2 (3x).
Differentiating both sides with respect to x, we get:
dy/dx = -12sin(3x)cos(3x)
Now, at x = π/6, we have:
dy/dx = -12sin(π/2)cos(π/2) = 0
This means that the slope of tangent to the curve at x = π/6 is zero.
However, having a zero slope does not necessarily mean that the tangent is vertical. In fact, the tangent will be vertical only if the function is not differentiable at that point.
To check if the function is differentiable at x = π/6, we need to check if the left-hand and right-hand limits of dy/dx exist and are equal.
Let's first find the left-hand limit:
lim┬(h→0-)〖(f(π/6+h)-f(π/6))/h〗 = lim┬(h→0-)〖(2cos^2(3(π/6+h))-2cos^2(3π/6))/h〗
= lim┬(h→0-)〖(2cos^2(π/2-3h)-2)/h〗
= lim┬(h→0-)〖(2sin^2(3h)-2)/h〗
= lim┬(h→0-)〖2(sin^2(3h))/(3h)×(3h)-2/h〗
= 0
Similarly, we can find the right-hand limit:
lim┬(h→0+)〖(f(π/6+h)-f(π/6))/h〗 = lim┬(h→0+)〖(2cos^2(3(π/6+h))-2cos^2(3π/6))/h〗
= lim┬(h→0+)〖(2cos^2(π/2-3h)-2)/h〗
= lim┬(h→0+)〖(2sin^2(3h)-2)/h〗
= lim┬(h→0+)〖2(sin^2(3h))/(3h)×(3h)-2/h〗
= 0
Since both the left-hand and right-hand limits of dy/dx exist and are equal to zero, the function is differentiable at x = π/6.
Therefore, the correct answer is option (D) A is false and R is True.
Explanation:
Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.
Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.
Explanation:
The given curve is y = 2cos2 (3x).
Differentiating both sides with respect to x, we get:
dy/dx = -12sin(3x)cos(3x)
Now, at x = π/6, we have:
dy/dx = -12sin(π/2)cos(π/2) = 0
This means that the slope of tangent to the curve at x = π/6 is zero.
However, having a zero slope does not necessarily mean that the tangent is vertical. In fact, the tangent will be vertical only if the function is not differentiable at that point.
To check if the function is differentiable at x = π/6, we need to check if the left-hand and right-hand limits of dy/dx exist and are equal.
Let's first find the left-hand limit:
lim┬(h→0-)〖(f(π/6+h)-f(π/6))/h〗 = lim┬(h→0-)〖(2cos^2(3(π/6+h))-2cos^2(3π/6))/h〗
= lim┬(h→0-)〖(2cos^2(π/2-3h)-2)/h〗
= lim┬(h→0-)〖(2sin^2(3h)-2)/h〗
= lim┬(h→0-)〖2(sin^2(3h))/(3h)×(3h)-2/h〗
= 0
Similarly, we can find the right-hand limit:
lim┬(h→0+)〖(f(π/6+h)-f(π/6))/h〗 = lim┬(h→0+)〖(2cos^2(3(π/6+h))-2cos^2(3π/6))/h〗
= lim┬(h→0+)〖(2cos^2(π/2-3h)-2)/h〗
= lim┬(h→0+)〖(2sin^2(3h)-2)/h〗
= lim┬(h→0+)〖2(sin^2(3h))/(3h)×(3h)-2/h〗
= 0
Since both the left-hand and right-hand limits of dy/dx exist and are equal to zero, the function is differentiable at x = π/6.
Therefore, the correct answer is option (D) A is false and R is True.
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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ample number of questions to practice Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): At x = π/6, the curve y = 2cos2 (3x) has a vertical tangent.Reason (R): The slope of tangent to the curve y = 2cos2 (3x) at x = π/6 is zero.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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