Question

1. Limitni hisoblang. a) lim x²=-3x X X-→1. 12.10.23y. b) lim h²+5h h=2 h 2. Funksiya hosilasini toping. the a) f(x) = x²= 5x³² +4 () f(x)=x²45X-3 3. Maddiy nuztaring berilgan to vagtelagi terligini toping a) ṣ(t) = t ² 2t²+t; t = 5. b) ≤(t) = 5€ +t ²+√²² · (o=4 4. Hosilani toping a)y=t+xv @) y = x ² + ²√/X²+- -_-) + ²x² 5. Funksiya ukwn wrinma tangla mosini tuzing. a) f(x) = 2² + ln²; X₁ = 1 f(x) = 2* / X₂=-2​

Answer 1

1. a) lim (x² + 3x) as x approaches 1. = 1² + 3*1 = 1 + 3 = 4

b) lim (h² + 5h) as h approaches 2. = 2² + 5*2 = 4 + 10 = 14

2. a) f(x) = x² - 5x³² + 4; To find the derivative, f'(x), you can use the power rule. f'(x) = 2x - 30x² + 0 = 2x - 30x²

b) f(x) = x² + 45x - 3; f'(x) = 2x + 45 - 0 = 2x + 45

3. a) Given ṣ(t) = t² - 2t² + t; t = 5. Calculate ṣ(5) = 5² - 2*5² + 5 = 25 - 50 + 5 = -20

b) Given ≤(t) = 5€ + t² + √(22) · (o = 4). Calculate ≤(4) = 5*4 + 4² + √(22) = 20 + 16 + 2√2

4. a) y = t + xv; It seems there's a typo, and the equation isn't clear. Please provide the correct equation for y.

b) y = x² + ²√(x² + _) + ²x²; The equation seems to have some missing values represented by underscores. Please provide the complete equation for y.

5. a) f(x) = 2² + ln²(x); X₁ = 1. To find the tangent line at x = 1, you'll need to calculate f'(1) and use the point-slope form of the equation of a line.

b) f(x) = 2* / X₂ = -2. Similarly, to find the tangent line at x = -2, calculate f'(-2) and use the point-slope form.

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