Limits and Derivatives
Madhya Pradesh Board · Class 11 · Mathematics
Flashcards for Limits and Derivatives — Madhya Pradesh Board Class 11 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Find the average velocity of a body dropped from a cliff during the first 2 seconds if s = 4.9t^2 metres.
Answer
Step 1: Use s = 4.9t^2. Step 2: Find distance at t = 2 s: s = 4.9(2)^2 = 19.6 m. Step 3: Distance at t = 0 s is 0 m. Step 4: Average velocity = distance ÷ time = (19.6 - 0)/(2 - 0) = 9.8 m/s. Answer: …
यदि s = 4.9t^2 metres हो, तो एक चट्टान से गिराई गई वस्तु की प्रथम 2 seconds में औसत वेग ज्ञात कीजिए।
Answer
चरण 1: s = 4.9t^2 का प्रयोग कीजिए। चरण 2: t = 2 s पर दूरी ज्ञात कीजिए: s = 4.9(2)^2 = 19.6 m. चरण 3: t = 0 s पर दूरी 0 m है। चरण 4: औसत वेग = दूरी ÷ समय = (19.6 - 0)/(2 - 0) = 9.8 m/s. उत्तर: 9.8 m/s.
What is the instantaneous velocity of the body at t = 2 seconds approximately?
Answer
Use the narrowing average velocities around t = 2 seconds. Values close to t = 2 give velocities between 19.551 m/s and 19.649 m/s. So the instantaneous velocity lies in this interval. Answer: between…
t = 2 seconds पर वस्तु का तत्क्षण वेग लगभग कितना है?
Answer
t = 2 seconds के आसपास के संकुचित होते औसत वेगों का उपयोग कीजिए। t = 2 के पास के मान 19.551 m/s और 19.649 m/s के बीच वेग देते हैं। अतः तत्क्षण वेग इस अंतराल में है। उत्तर: 19.551 m/s और 19.649 m/s के …
Why does the slope of the tangent represent instantaneous velocity?
Answer
The distance-time graph shows how displacement changes with time. For smaller and smaller time intervals, the slope of the chord approaches the slope of the tangent. That limiting slope gives the rate…
स्पर्शरेखा का ढाल तत्क्षण वेग का प्रतिनिधित्व क्यों करता है?
Answer
दूरी-समय ग्राफ यह दिखाता है कि विस्थापन समय के साथ कैसे बदलता है। छोटे और छोटे समय अंतरालों के लिए, जीवा का ढाल स्पर्शरेखा के ढाल के पास पहुँचता है। यह सीमांत ढाल एक क्षण पर परिवर्तन की दर देता है। अत…
Find lim x→5 of f(x) = x + 10.
Answer
Step 1: Substitute x = 5. Step 2: f(5) = 5 + 10 = 15. Step 3: Since the function is linear, the limit equals the function value. Answer: 15.
lim x→5 of f(x) = x + 10 ज्ञात कीजिए।
Answer
चरण 1: x = 5 रखिए। चरण 2: f(5) = 5 + 10 = 15. चरण 3: चूँकि फलन रैखिक है, इसलिए सीमा फलन के मान के बराबर है। उत्तर: 15.
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