Find the absolute maximum and absolute minimum of the function f(x)=3sin(x)cos(x) over the interval [π/2,2π].

Q: tution for each of the following indefinite integrals. To input inverse trigonometric functions use…

A: We have to substitution

Q: Given the vector i = (2,0, 1). (a) Solve for the value of a so that u and o= (a, 2, a) form a 60°…

A: Given the vector u→=2, 0, 1.a To solve for the value of 'a' so that u→ and v→=a, 2, a form a 60°…

Q: Find the Taylor polynomial of order 3 generated by fat a. f(x) = x2 +x+1, a=2 O A. P3(x) =7+5(x- 2)…

A: f(x)=x2+x+1f(2)=4+2+1 =7f'(x)=2x+1f'(2)=4+1 =5f''(x)=2f''(2)=2f'''(2)=0

Q: . Use L'Hospitalľ's Rule to evaluate lim t In 1+

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Q: 2. Find the Area bounded by the curve y = 4-x? and the x-axis.

A: Topic = Area

Q: Find the area of the region in question Area =

A:

Q: dx 2+

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Q: 4 sec t to evaluate the integral J 2-16 dx Use the substitution x = Note: Use C for an arbitrary…

A:

Q: The size of an unborn fetus of a certain species depends on its age. Data for Head circumference (H)…

A: Let's find.

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) = - M1+tanh 2 satisfies the…

A: Here, the given function is: y(t)=12M1+tanhk(t-a)2...(1)

Q: 3) (0,1,0), (2,1,0), (3,4,7) Ans. Indepena

A: Given

Q: Fill in the blanks: Answer only no need explanation. 1. The derivative of a constant ______ 2. The…

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Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: The objective of the question is determine Mn.

Q: 2л + 3 dx 4г2 — 4х + 5

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Q: Write the Taylor series for f(r) = a about z = 4 as en(x-4)". %3D Find the first five coefficients.…

A: The Taylor Series of f(x)= x3 with center a=4

Q: sin(x²) Evaluate lim 140- e2r – 2x – 1

A: Topic = Limits

Q: Find the genekat Sotutionsto the differentiat -or Special

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Q: f(e) =. Find the Taylor series, centered at c = 5, for the function f(z) 00 Σ f(x) = n-0 The…

A: Solution is given below:

Q: Find the curve whose slope at any point (x,y) is 6x^2−2x−5 if the curve is required to pass through…

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Q: Find the area of the region described. - 3 The region in the first quadrant bounded by y =x and y= 3…

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Q: 9–x² x2

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Q: 3x + 5 dx, ] (x + 1)(x – 3)²

A: ∫3x+5x+1x-32dx

Q: II. Find the Inverse Laplace of the following 1 a. s2+6s+25 s2 b. (s-1)3 7 5 6 С. s4 8 s3 s2

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Q: Question 3 Compute V31.6 approximately by use of differentials. 1.098 (E) None of the choices 1.890…

A: 31.65=1.995

Q: Given f(x) = (2x – 3)' (x +1). Determine (if any) (i) Critical point(s) for f(x), (ii) The interval…

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Q: solve 4cos^2(x)-13cos(x)-12=0 for all solutions 0<=x<2pie

A: We can find the solution as below.

Q: An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If the oil was…

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Q: following integration can be solved by using the     technique, where in the first application of…

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Q: d se dx 1 (x) = to find the derivative of the inverse at the indicated point. 1 t f(x) = – 5x° + 5,…

A: Topic:- application of derivatives

Q: nd the sum of the following series. If it is divergent, type "Diverges" or "D". 3n 5"n! nswer. ote:…

A: To find the sum of the series.

Q: Determine the Laplace transforms of 3, 0 12

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Q: (b) Evaluate each of the following integrals ) || sin(z+ y)dzdy where R= |0,1] × [0,1] (i) evdA…

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Q: sin x ferentiate y = (x² + 1)°

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Q: Find the equation of the tangent line to the graph of the functionf(z) sin (3,/7) at the point…

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Q: 7. Simplify and evaluate. (2x³y²)³ a) (x’y (9y)? b) for y=-2 (3y*)

A: Given: a)2x-3y23x3y-42b)9y23y-13

Q: sin(x²) 1+0- e2r – 2x – 1° Evaluate lim |

A: The objective of the question is evaluate the limit.

Q: Find the following antiderivatives. Cosh sinh r - 1 cosh r dr (a)

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Activity 2. Answer the given problem. The population P(t) of a bacterial colony t hours after…

A: We have to find population of bacteria at t=12 hours.

Q: 2. of the image graph in terms of x? y 2-3 C. y= 2(1-x+2|- 3) D. y= (1-2x+ 2|-3) A. y= -|2x +2|- 3…

A: Consider the graph

Q: Slove this equation -2/x e y dx =1 1 x / dy

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Q: Find the Taylor series generated by f at x= a. f(x) = -, 1 a = 3 X (x- 3)" Ο Α Σ 3" OA. n =0 (x –…

A: We have to find the Taylor's series for given function at a=3 . For this all order derivatives of f…

Q: -5x- 4 etermine an equation of the inverse of the function y = 6x +4 y = -5 -5x +6 C. リ= -4 6x-4 y =…

A: Given query is to find the inverse function.

Q: Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is…

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Q: Solve the following initial-value problem. f′(x)=2 3√x+3x^2, f(0)=6

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Q: 2. Evaluate ř(t) dt: 4 4t ř(t) t2 + 5t + 6' î + 2e4t cos t j - k; a = 0 and b = 4 t2 + 1

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Q: 2r 2r If the total volume of the cylinder and square block is 30 cm', express h in terms of r.

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Q: 3:) Consider the function g defined by g(x ,y) = cos (TXVG) + logg (x-y) 3 (b) calculate the…

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Q: 3. Consider the vector field F(x, y) = (2xy, x2 - sin y). Evaluate %3D F. ds where C is the curve…

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Q: Suppose f(x) = ex, xE[0, 1]. (a) Find the slope of the secant line connecting the points (x, y) =…

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Q: Suppose that h = 2x'y, where both x and y are changing with time. At a certain instant when x = 1…

A: