1. Let f(x) be the cubic function graphed below and g(x) be the quadratic function graphed below. Write an expression in terms of f(x) and g(x) that gives the area of shaded region between the two curves. You do not need to find the equations of the curves. f(x) g(x)

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Q: A bacteria culture starts with 500 bacteria and doubles in size every half hour. (c) How many…

A: Topic:- exponential growth function

Q: x³ cos x dx

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Q: Problem 2. Consider the lines 1(t) and r(s) defined below. l(t) = t+ r(s) = 8+ Your buddy Ron…

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A: I am attaching image so that you understand each and every step.

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A: Solution: L-1 {1/s7}

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Q: a body at a temperature of 50°F is placed in an oven whose temperature is kept at 150°F. If after 10…

A: We can use differential equation or Newton law of cooling to solve the problem

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Q: Which of the following is linear equation? a. 3x + 2y-z² = 0 b. sin 2x + y = 1 c. log x + 2y = 2 ww…

A: The equations are To evaluate: The linear equation.

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A: Given problem:- Find the solution of the following differential equation.  (yx + xycot x) dx + xdy =…

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A: Washer Method : Suppose that the f(x) and g(x) are continuous and non-negative function on a,b and…

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Q: 10x3, 5-x, = x < -2 x ≥ −2 Let f(x) 1. f(-2)= 2. lim f(x) = x→→2+ 3. lim f(x): = x→→→2 4. lim f(x) x…

A: The solution of 4 and 5 are given in the next steps.

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Q: Find the function y = y(x) (for x > 0) which satisfies the separable differential equation dy 8 +…

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Q: Consider the following integral. fx²√³+1 dx Identify the definite integral that will result after…

A: topic- indefinite integral

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Q: 9. Find the area of the surface generated when the given arc is revolved about the x-axis: 4x² +…

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Q: Solve the initial value differential equation with initial values y(0)=2 and y'(0)=6 y" - 3y + 2y =6

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Q: ·S √ 6. dx x² - 4x + 13

A: ∫1u2+1du = lnu+u2+1+C

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A: The number is  168.  The character after 16 is 8.

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A: Given, (x1,y1)= (100,-40) (x2,y2)= (20,-5)

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A: here is given that sin-1(1/2) we now that sin-1(sin(π/6))

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Q: 57. If f(x) = (A) (0,00) fen²x + (n (ex) (n² (ex) dx; f(1) = 0 and g(x) = 1 -f(x). Then the domain…

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Q: The ellipse 3 4 8 16 x²y² 1 = + 9 16 4 has a vertical axis of

A: elipse equation is given  x2/9 + y2/16 = 1/4 here compare with  x2/a2 + y2/b2 = 1

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Q: X912 65. f dx is equal to - √1+x" (A) = log(x² + √√x+1)+c 7/2 (C) 2√1+x" +c HT (B) log +C x" 11/2…

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Q: 48. If L = lim (cosec x)/(x, then the value of nL is - X->0* (A)1 (BY-1 (C) 0 (D) none of these

A: To evaluate: L=limx→0+ (cosec⁡x)1/ln⁡x Taking ln both sides, we will get ln L=lnlimx→0+…

Q: Use the second fundamental theorem of calculus to evaluate the following: x, x 20 10. [* f(x) dx if…

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Q: See

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Q: - Find the volume of the region cut from cylindrical (x² + y² = 16) by the plane z 0 and the plane…

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Q: 5. (a) Find the particular solution of the differential equation x³ = 1-e²t if x(0) = 2.

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Q: If y(z) = √3+ rºdr then 0 y' (2) = 524√√3+25 Q X estion E

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Q: If lim f(z) = 2 and lim g(x) = 7, then lim[3ƒ(z) — 4g(x)] = -22 G- *-b Ⓒ True O False

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Q: Find the vector equation of the line between the points (3, -1, 2) & (1, 4, -1), then graph the…

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Q: udv = uv J to Explain why the substitutions below are inappropriate. Let u = e 1. Suppose we apply…

A: Here, to evaluate: ∫xexdx using integration by parts.