Calculus

Factoring grouping and cubic polynomials Questions & Answers 3x³ - 5x² - 9x + 15 - ANSWER: (3x - 5)(x² - 3) 8x³ + 125 - ANSWER: (2x + 5)(4x² - 10x + 25) 16x² -121y² - ANSWER: (4x - 11y)(4x + 11y) 27x³ − 125 - ANSWER: (3x - 5)(9x² + 15x + 25) 64x² -25y² - ANSWER: (8x - 5y)(8x + 5y) ...

Factoring Perfect Square Trinomials Question & Answers (x-1)² - ANSWER: x²-2x+1 (x-2)² - ANSWER: x²-4x+4 (x-3)² - ANSWER: x²-6x+9 (x-4)² - ANSWER: x²-8x+16 (x-5)² - ANSWER: x²-10x+25 (x-6)² - ANSWER: x²-12x+36 (x-7)² - ANSWER: x²-14x+49.................................

Calculus (1) Solutions -cos(x)+C - ANSWER: -cot(x)+C - ANSWER: -csc(x)+C - ANSWER: -csc²(x) - ANSWER: -ln(cosx)+C = ln(secx)+C - ANSWER: hint: tanu = sinu/cosu -sin(x) - ANSWER: ∫1/(1+x^2)dx= - ANSWER: tan⁻¹x+C ∫1/(1+x^2)dx= - ANSWER: tan⁻¹x+C ∫1/(a^2+x^2)dx= - ANSWER: (1/a)(ta...

Calculus 1 Questions & Answers -1 - ANSWER: cos(π) -csc²(x) - ANSWER: -sin(x) - ANSWER: [s(b)-s(a)] / (b - a) - ANSWER: Average Velocity −√2/2 - ANSWER: cos(5π/4) −√3/2 - ANSWER: cos(7π/6) −1/2 - ANSWER: cos(4π/3) √2/2 - ANSWER: cos(π/4) √3/2 - ANSWER: cos(π/6) 0 - ANS...

Calculus 1 Questions & Answers (cos x-1)/(x) - ANSWER: 0 (d/dx)[f(x)+g(x)]=f'(x)+g'(x) - ANSWER: true (sin x)/(x) - ANSWER: 1 [a*u(x)+b*v(x)]'=a*u'(x)+b*v'(x) - ANSWER: true A continuous function has a relative minimum at c if and only if the function changes from decreasing to increasing...

Calculus 1 Questions & Answers (at some point) instantaneous Rate Of Change = - ANSWER: average Rate Of Change (hyperbolic sign) coshx = - ANSWER: (e^x + e^-x)/2 (hyperbolic sign) sinhx = - ANSWER: (e^x-e^-x)/2 & = - ANSWER: x distance #/0 - ANSWER: -infinity, +infinity, or DNE 1. factor 2. p...

Calculus 1 Questions & Answers 1 + cot^2θ = - ANSWER: csc^2θ A function is not a function if it does not pass ... - ANSWER: the vertical line test (each element x in a set D has exactly 1 element denoted f(x)) a) a corner b) a discontinuity c) a vertical tangent - ANSWER: Where can a derivat...

Calculus 1 Questions & Answers Absolute Extrema - ANSWER: Includes both absolute maximum and absolute minimum in a given interval. Absolute Extrema - ANSWER: Includes both absolute maximum and absolute minimum in a given interval. Absolute Extrema - ANSWER: May occur at critical points or endpo...

Calculus 1 final Questions & Answers - ANSWER: - ANSWER: 4 shapes of a curve - ANSWER: concave up: left hand is decreasing right hand is increasing concave down: left hand is increasing right had is decreasing a function f is continuous at a iff f(x)=f(a) - ANSWER: 3 requirements 1. f(a) is ...

Calculus 1 Overview Questions & Answers (d/dx)(f⁻¹(x)) at x=b - ANSWER: 1/(f'(f⁻¹(x)) -or- 1/f'(a) where b=f(a) Acceleration - ANSWER: derivative of velocity (second derivative) Antiderivatives - ANSWER: F'(x)=f(x) Antiderivatives and Area - ANSWER: Displacement: ∫v(t)dt , [a,b] -- s(...

Calculus 1 - Midterm #1 Questions & Answers Acceleration of a Function - ANSWER: Find the second derivative Chain Rule - ANSWER: F(x) = f(g(x)) F'(x) = f'(g(x)) - g'(x) Chain Rule Example #1 - ANSWER: f(x) = sin(1/x^2) f'(x) = cos(1/x^2) • (-2/x^3) Chain Rule Example #2 - ANSWER: e^(7x) ...

Calculus 1 Final exam review Questions & Answers (f /g)' = - ANSWER: (f'g-fg')/g^2 (f + g)' - ANSWER: f' + g' (fg)' - ANSWER: f'g + fg' area function - ANSWER: Let f be a continuous function, for t≥a. The area function for f with left endpoint a is A(x)=∫(^x∨a)f(t) dt, where x≥...