Consider the function: f(x) = 5x* – 2x³ + 3 Show that there is a value a e [0,2] such that f (a) = 15.

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A: Solution is given below:

Q: Problem 6 Use the rules of differentiation to to find the derivatives of the functions: (a) f(r) =…

A: topic- differentiation

Q: 1. Disk Method a. y = x2,x = 0, x = 2, y = 0, about the x ахis а.

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Q: x/2 dy 2. -y=e

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Suppose that f(x, y) = x? – zy + y² – 3z + 3y, with domain D constrained by the lines y = z, y = 0 ,…

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Q: find eigenualy gse for -57 to -구 -4 26

A: I have appended the formula used in the solution part.

Q: Find the area of the shaded region below. x = y? – 4y (-3, 3)

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Q: Evaluate dx 2 1-x

A: We have to evaluate ∫23x1-xdx. We know that ∫dxx2-a2 = 12aln x-ax+a+C

Q: Find the general solution of the differential equation. (Use C for the constant of Integration.) dy…

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Q: 2. Determine if the following integral converges or diverges. If the integral converges, find its…

A: We need to check whether the given integral converged or diverges.

Q: Evaluate: | V12 – 2| +x dx

A: Explanation of the answer is as follows

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Q: Evaluate the integral: V2 1 5xdx *Input answer as a decimal. Round-off to 2 decimal places.

A: The final answer is rounded off to 2 decimal places.

Q: The volume of a cube is increasing at the rate of 21 cc/min. At what rate is its surface area…

A: The volume of a cube is increasing at rate, dVdt = 21 cc/min To evaluate: The rate at which the…

Q: Find the indefinite integral. Check your result by differentiating. 10x dx Step 1 Observe that is…

A: ∫un du =un+1n+1+C

Q: d the volume of the solid whose base is the region enclosed by y = x² and y = 2, and the cross…

A: Topic:- application of integration

Q: Q2 ) Use the Simpson's rule with (n = 4) to estimate thef²n sinx dx . 2

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Q: Classify the statement as either true or false. lim 6= 7 x7 Choose the correct answer below. false…

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Q: Bob starts at home and for the next 4 hours he jogs along a straight path with a velocity function…

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Q: only

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Q: rounded to the nearest hundredth as needed.)

A: We have to find the producers surplus according to the given information

Q: Q2: Solve the following linear differential equation: y' + y = x+

A: We can solve this as follows:

Q: Solve cos (w) - 6 sin(w) for all solutions 0 < w < 27 %3D w = Give your answers accurate to 2…

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Q: ** Solve the following problem by setting up a linear system (remember to describe your variables)…

A: T=touchdown    6 pointsF=Field goals   3 pointsE= Extra points  1…

Q: Consider a rectangle with the following property. Perimeter: 112 meters Let w represent the width of…

A: A rectangle has perimeter 112 meters.

Q: Find the volUme OF the solid obtained by rotating about the y-axis the region boUnded by y= x° the…

A: Follow the procedure given below.

Q: R is the region bounded by the lines y = x, y = -x, and x = 1. %3D

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Q: Solve the given DE: dy e* – 2x cos y eу — хx2 sin y' dx ||

A: Differential equations is solved.

Q: Q4: Solve the following exact differential equation: 2xydx + (1 + x2)dy = 0

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Q: dx 1. Evaluate the integral -∞ 1+x² 2. Evaluate the integral •x+y So SL** (x + y+ z) dz dy dx.

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Q: Find dx in each of the following. dx2 x= e' cost b. y=e' sint a. y = t-1

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Q: 2. y =,x = 1, x = 4, and y O is revolved about the y – axis. (Answer: 247 c. u. )

A: Given: y=4x, x=1, x=0 and y=0   The bounded region is as shown below.     Apply the cylindrical…

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A: answer is in next step

Q: Find the slope of the line tangent to the curve y =x-2x+ 1 at x 1 01 O 1/2 O 1/3 O 1/4

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Q: The limit lim (x c 1 X• COS is an indeterminate form of type 0· o. Select one: True O False

A: Given: limx→∞x·cos1x   As we know that; limx→afx·gx=limx→afx·limx→agx

Q: "(x) If t(x) = Vx find ť'(x)" -2x O 2x -1/2x O 1/2x O None of these O o o o

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: y = 5x2 – 3x – 4 | | Finding the derivative of y: y = 5x? – 3x – 4 y' = 10x – 3 Finding the…

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Q: Find the area bounded 1. 2x2 + 4x + y = 0 , y = 2x 2. y = x³,y = 4x²

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Q: Given y = u28 and u = 5– 3x?, find dy/dx. A. = 168x(5 - 3x?)27 D. dx = -28x(5 – 3x²)²7 dx dy В. dx…

A: As we know that; The Power law: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2   (1). Given: y=u28…

Q: x²(3 –4x)dx -4 318 338 358 378 None of the Above

A: Given: I=∫-4-1x23-4xdx   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: 2 v2x-x2 XY xydydx 0 0

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Q: 1/2 dx 1-х4

A: Let 1-x4 = t

Q: Rewrite the expansions in terms of exponential and simplify the results as much as you can. 1. 2…

A: We use the formula of coshx and sinhx to simplify the given expression.

Q: The limit lim x · In cos エ→0 is an indeterminate form of type 0 ·o. Select one: O True O False

A: LetL=limx→∞ xlncos1xL=∞.ln(cos(1∞))L=∞.ln(cos(0))L=∞.ln(1))L=∞.0Which is undefine

Q: sin (x-1) lim x+1 x2+2x-3

A: To evaluate: limx→1 sin⁡(x−1)x2+2x−3 The given limit is of indeterminant form 0/0

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Q: The temperature at which water starts to boil (its boiling point) is linearly related to the…

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Q: 14. %24

A: For determining the continuity of a function from its graph , we need to examine whether the graph…