Question

can u please help me with both of these, thanks

Let g(x) = x3 + x. Compute g(x+h)-g(x).( h

Answer 1

soin :- given, gin) = n3th ginth)- gin) = ? h To find ginth) simply supositi substitute n=nth in the function gen) Thus, gluth) = (x+h)3 +14th) genen) = (reth fath)2 +13 genth) = (th) { x² + 2xhth 2+13 genth) = x² + 2x²h tun? tutu²n + anh? th?th genth) = n3 +24²h tu h²+utu²h + 24h2th3th

Now, g(x+h)-gR) MC 3+2 4 ²h+nh²+ nth tn +2442 th3th - (3 + x) h gluth)-gin) + 2n²h tun? +4²n +x+ 2062 th3th x ginth)-ging = 2.4²h.tuh²+ n²n + 2xh² th3th h h - hl2n²+ nh+ ²) = y (2x²+4h+n²+ 24h th?+1) genth) - Jin) h b genth)-gin) = 20² + x2 + 24h to.hth 2+1 genthy-gen) = 3n2+3nhth²+1 hence, ginth)-gen)= 34² +34 h th ²+1 Ans

soint given, coso = ㅎ TO<3 2 since coso=1-asin 20/2 asin 20/2= I-coso sin 2012 = In cosa 2_ Now, 1 sin ²0/2 = 1 "- 1 - / 8 2 sin 20/2 St1 8. 9 2 16 sin 012= 56 3. + 3 4 since TLOL 3 IT To 2 3T 4 2 le 0% is in quadrant i and in quadrant sin is positive. G hence, sin 0/2 3 Ans

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