Exponential and Logarithmic Functions 11. Use the properties of logarithms to fully expand the logarithm into the sum or difference of multiple logarithms 2 3 10g, (²:1²) logb Z

Q: Q4/Find x and y that make the equations equal to zero: 5x+2y-4-0 6x+8y-2-0

A: Simplify both equation for x and y .

Q: Q2: The population of a state is known to grow at a rate proportional to the number of people…

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Q: Let y = tan(5x + 2). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

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Q: 1. Evaluate the given integral Q. y/3 9-y² - 1.² [ord ³* 0 0 0 Q Your answer (1-2) dz dx dy

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Q: x = y² - 2y and x = 4y - y²

A: The given curves are; x=y2-2y and x=4y-y2 Now find the point of intersection between the given…

Q: Limits 8. Find the indicated limit using the graph of f(x) below. , V lim f (x) x-2 =

A: Topic = Limits

Q: L 1 1 {}} 2 S S + 1 S-6

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Q: Q9: The Law of Sines ( a) Given: B = 10° C = 135° c = 45 Find: A-? a-? b-?

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Q: 8- Find the derivative of (x²+1)x

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Q: Find the points on the cardioid r = sin(2θ) where the tangent line is horizontal. Draw.

A: We have to draw the cardioid r=sin(2 theta)  And find the point where the tangent line is…

Q: 2. (yx + xycot x) dx + xdy = 0

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

Q: The points A(3, 0, 1), B(2, 0, 2) and C(3, 1, k) form a triang area Determine the value(s) of k for…

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Q: dx (4+x²)² √

A: Explained below

Q: Determine the maximum and minimum of each function on the given interval 9 a. f(x) = x³ - 12x + 2,…

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Q: ·S √ 6. dx x² - 4x + 13

A: ∫1u2+1du = lnu+u2+1+C

Q: (-1)kk Determine whether the series converges absolutely, converges conditionally, or diverges Σk=1…

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Q: If your get car get 32 miles per gallon, how much does it cost you to drive 30 miles when gasoline…

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Q: It is easy to check that for any value of c, the function C y = x² + is a solution of the equation…

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Q: The height y (in feet) of a ball thrown by a ch 1 -x² + 6x + 5 - y = 14 where is the horizontal…

A: The height of the ball is given by  y=-114x2+6x+5 in feet where x is horizontal distance from child.…

Q: The function f(x) = 7 1+9x² f(x) = Σ cnan. n=0 Find the first few coefficients in the power corios…

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Q: 29. Verify that the piecewise-defined function 1-x², x<0 x ≥ 0 is a solution of the differential…

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Q: If you were to use a substitution of u = integration be? (Enter an exact answer.) Provide your…

A: We have to solve integral

Q: 2) Sketch the solid whose volume is given by the integral  and evaluate the integral. ∫0 to pi/2 ∫0…

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Q: The Kirk Kelly Kandy Company makes two kinds of candy, Kisses and Kreams. The profit, in dollars,…

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Q: Find the area bounded by the parabola x=8+2y-y², the y-axis, y=-1, and y=3 A) 92/3 s.u. B) 92/4 s.u.…

A: A detailed solution is given below.

Q: 1-x² 1-x 10 f(x, y, z) dy dz dx

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Q: Q4: Let y=√ and 1= x² then y) = 0 if n= a) 2 b) 3 c) 4 d)5 e) others

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Q: Let f(x,y) = 3x4 - 4x³y + 2x2y2-y. Let f, be the partial derivative of f(x, y) with respect to x.…

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Q: MATHS HOME A 41. If f (x) = f[ta (A) 3-e^/4 4 J'a (B). tan((nx) +- dx & f(1) = 0, then f (e/4) is -…

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Q: Q1/ The volume generated by rotating the region bounded by the given curves y = √x + 1 + 2, y = 2x,…

A: Concept: The disk method: The volume of the solid created by rotating the region enclosed by the…

Q: Let S (x,y) = 3e³x² +2e³x+5y + 4e'y?. Find fy A 3e'x4 + 10e³x + 5y + 28e¹y6 12e x³ + 6e³x+5y + 4e¹y7…

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Q: find dy dx ² +F y = 3 casch + Cosa 3 and x = Sin²³ o

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Q: Solve y'' - 2y' + y = 0, y(0) = — 5, y'(0) = = y(t) = - 8

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Q: Use linear approximation, i.e. the tangent line, to approximate √81.3 as follows: - Let f(x) √x.…

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Q: Find dy/dx:

A: We have to solve the dy/dx using fundamental theorem of calculus.

Q: Test the series for convergence O a. the series diverges O b. the series converges ∞ 3k k-1!

A: We need to evaluate the convergence of the series :

Q: Find the value of k for which the constant function (t) - =k is a solution of the differential…

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Q: S= S stozx 1 secy tan: Sinx cas 2. S

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Q: At 12:00 noon, there were 200 bacteria present. By 4:00 pm, there were 379 bacteria. If the bacteria…

A: At 12.00 noon, there were 200 bacteria present.By 1:00 pm, there were 379 bacteria.

Q: Use multiple application of simpson's 1/3 rule to numerically in- tegrate: f(x) = 8 + 5 sin (x) 0 to…

A: We need to use Simpson's one third rule.

Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

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Q: Direction: Fill in the blanks with the next step in solving the solutions of the differential…

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Q: Let f(x, y) = x³ + y³ - 2x²y². Calculate fa, fy, fax, fyy and fry. Hence show that (3/4, 3/4) is a…

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Q: If f(0) = -6, f'(0): = 3 S³ = x. f''(x) dx = = - 20, f(3) = 297 11 and f'(3) X 18 then: -49

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Q: L 4s 2 4s² + 1

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Q: 45. I= (A) 2 (C) 3 +c, then f '(1) is equal to - 14 2 2-x ปี = √/²=Xx dx = ²√ √/²² (x) + c (B) 1…

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Q: Evaluate the integral T 22 P" sin cos e de dode Hd 0 H₂

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Q: Find the order and degree of e^y" - 3(y¹)² + 2xy = xe² and write the differential equation in noxmal…

A: Follow the procedure given below.

Q: Find

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