1) BASIC DERIVATIVES: Differentiate and simplify the following functions a) f(x) = 5x³+3x² - 5x+2 b) f(x)= √√x-6√x

Q: Write the following numbers in Cartesian form (i.e., in the form a + bi). Use the principal value…

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Q: (c) To solve this by calculus, we'd need to calculate substitution u = 1- x² doesn't seem to help.…

A: To explain briefly why the substitution , does not seem to help  to calculate the integral .

Q: For an object whose velocity is given by v(t) = - +4, what is its displacement on the interval t = 0…

A: Given that valocity v(t) = - t2 +4. And interval is t=0 to t=3. We find displacement on this…

Q: 3. As light passes through water, it is gradually absorbed. The percent of light absorbed, 4, as a…

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Q: Determine all values of p for which the improper integral converges. [.. 7 dx Op> 1 Op≥ 1 Op<0…

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Q: Express the set in interval notation. 3 Select one: O a. [3,9) O b. (3,9] O c. [3,9] O d. (-∞,3) 9

A: The number line represents the solution  the aim is to find the solution in interval notation

Q: (a) ㅣ dr x(x - 1)3

A: The given integral is:I=∫dxx(x-1)2

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A: ∫xndx=xn+1n+1+C ∫1xdx=lnx+C

Q: Given the matrices A and B, solve for X. 5X - B = A. 5 A: - [31]-[9] = and B = -4 Select one: a. O…

A: A = -35-3   -4   ,   B = -3  4-355X-B = A

Q: Evaluate the sum 1 Σ² n! n=0 1 + (-1)^²+¹ + (-2)' (−1)n+1 n 2n+1

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Q: Solve the initial-value problem for x as a function of t. dx (t2-10t+24) dt SAN 1, (t > 6, x(9) = 0)

A: Use the separated the variable

Q: (x² + x)ex³+³x dx

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Q: Bus Econ 14.1.89 ¤ In order to study the effects of World War II on a certain country's economy, an…

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Q: 0. 23. L₂ (x² + x) dx

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Q: 4. Show that det(AB) = det(A)det(B) for A ===[₂]

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Q: The following table gives the millions of metric tons of carbon dioxide emissions in a certain…

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Q: The position function of an object is given by s(t) = 16t², where s(t) is the height in feet and t…

A: We know that the speed formula ds/dt

Q: Find the Laplace tranform of the ff: 2x2

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Q: Let f(x, y, z) = 3x6y + 2xy + 4yz7. Find the requested iterated partials. (Use symbolic notation and…

A: f(x,y,z)=3x6y+2xy4+4yz7

Q: Evaluate the improper integral or state that it diverges.

A: We need to evaluate the following integral: ∫-∞-48x3dx This can be computed as follows:

Q: Speed of Parametric particle. x=+³²-3+² y = 26²³-3+² -12 +

A: We have  3t2-6t2+6t2-6t-122=375 We have to solve for 't'

Q: SLO C. Use parametric equations and polar coordinates to graph, differentiate and integrate…

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Q: 1. The function is given piecewise: ƒ(x) = cos(x) 0 X if x 0

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Q: Suppose f(x, y) (a) ▼ f(x, y) = (b) ▼ f(-1.1, 6): = tan(x) + y and u is the unit vector in the…

A: f(x,y)=sqrt(tanx+y) , (x, y) = (-1.1,6) Unit vector in the direction &lt;-1,1&gt; Find the gradient…

Q: Given the polar equation r = The eccentricity is e = 5 The equation of the directrix is: 7 6 sin(0)'…

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Q: 7. A lidless large steel fuel tank is cylindrical in shape. To optimize storage in the truck, the…

A: A lidless large steel fuel tank is cylindrical. To optimize the truck, the total volume of the…

Q: Using row operations, find the inverse of this matrix. 1 -2 -61 [6] 01 5 001

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Q: Use integration by parts twice to evaluate fet cos(3t)dt: Step 1: Let u = et and du + S fet…

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Q: Consider the graph of the function f given below. f(x) I -2 4 B) If h(x) 2 0 -2 2 x 4 A) If g(x) =…

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Q: Use the Binomial Theorem to expand and simplify the expression. (2-3x) 3 2 -27x + 54x 18x + 8 -27x³…

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: The expression √(3x - 2√x) equals Ax³/2. + Bx where A equals: and Bequals:

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Q: Determine whether the improper integral diverges or converges. O converges O diverges dx Evaluate…

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Q: Here is a 45-45-90 triangle. 10√ 2 ft Find the lengths of the missing sides. Enter the length of the…

A: The 45-45-90 triangle rule states that the three sides of the triangle are in the ratio 1:1:√2, here…

Q: In Calculus you will see the symbol y'. Treat y' as a variable and solve the equation for y. 6y²y +…

A: To solve the following equation for y'. 6y2y'+30xy+6x2y'=5y2+25xyy'

Q: Simplify the expression. ✓-25 √9 Select one: √5 3 a. O b. O c. O d. -- Wher wher 5 3 3 i

A: The expression is given by -259 To determine: The simplified expression.

Q: A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will…

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Q: Find the maximum value of the function f(x,y)=2x^2+3y^2-4x-5 on the domain x^2+y^2=121. List the…

A: To find the maximum value of the function fx, y=2x2+3y2-4x-5  on the domain x2+y2=121. To list the…

Q: Given: (x-2)29+(y-4)216=1What is the center? (0,0) (2,0) (0,4) (2,4)

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Q: Evaluate the integral. (Use C for the constant of integration.) [7t sin 7t sin²(t) dt

A: Explanation:-

Q: A particle that moves along a straight line has velocity v(t) = t²e-8tm/s after t seconds. This…

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Q: (x(t) Find a plane containing the point (2,-4,-2) and the line y(t) z(t) = = = 2 - 5t 4 - 3t 5- 4t

A: Equation of the plane general form is  a(x-x_1)+b(y-y_1)+c(z-z_1)=0

Q: Use a combination of substitution and parts to evaluate the integral sin(7√x)dx: Step 1:…

A: We have to find integration of above question.

Q: Suppose that a savings account pays an effective rate of interest of 10.2 percent. What is the…

A: Suppose that a savings account pays an effective rate of interest of 10.2 percent. What is the…

Q: Calculate the Taylor polynomials T₂(x) and T3 (x) centered at x = a for f(x) = 20.sin(x), a =…

A: Here we have given a function: fx=20sinx, a=π2 So, here we need to calculate the Taylor Polynomial…

Q: For each of the following infinite series, determine whether the series is absolutely convergent,…

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Q: Making this substitution using [₁ gives us 10 sin²(x) cos³(x) dx 10 10 sin²(x) (1 - sin²(x)) cos(x)…

A: To evaluate the following integral. ∫10 sin2x cos3x dx Note: After seeing the previous solution, we…

Q: (a) Use a calculator to find e0.7(rounded to five decimal places). eº.7% (b) Estimate eº.7 by using…

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Q: Evaluate the definite integral foto tº cos(t5)dt: 5/π/2 Step 1: Start by making the substitution…

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Q: Problem 11 Express the function f defined below using step functions and find its Laplace trans-…

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