के मान निकालिए, जहाँ
से प्राप्त वक्र है।
दिया गया प्रश्न है: \[ \int_C (2x^2 + 3y^2) dx \] जहाँ \( C \) से वक्र \( x(t) = at^2 \) और \( y(t) = 2at \), \( 0 \leq t \leq 1 \) द्वारा परिभाषित है। अब हम इसका समाधान करेंगे। ### चरण 1: समीकरण में पैरामीट्रिक रूप में सब्सटिट्यूट करें वक्र \( C \) को पैरामीट्रिक रूप में परिभाषित किया गया है: - \( x(t) = at^2 \) - \( y(t) = 2at \) _______ ___ ______ _______ _______ ________ _________.
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वक्रो y = 4x2 और 4 से पसिद्ध और (x, y) के गात वाजे एक पतली सीट का गुरुत्व केन्द्र ज्ञात कीजिए।
Use double integration of find the volume of the ellipsoid
Let the function f be defined by
Show that f has directional derivatives in all directions at (0,0).
दितः समाकलन का प्रयोग करके दीर्घवृज
का आयतन ज्ञात कीजिए।
Using the Implicit Function Theorem, show that there exists a unique differentiable function g in a neighbourhood of 1 such that g (1) = 2 and F(g( y), y) = 0 in a neighbourhood of (1,2), where
defines the function F. Also find g′( y).
Does the function
satisfy the requirement of Schwarz’s theorem at (1,1) ? Justify your answer.
Find the domain and range of the function f , defined by Also find two level curves of this function. Give a rough sketch of them.