I 2ex e3x tex dx

Q: Evaluate: if vector OA = (2,3) and OB (-1,-2) Show all steps please

A: if a vector is of the form  a→=a1,a2  then a→=a12+a22 see  below the answer

Q: 10) In an aquaculture, the amount of bacteria doubles every 7 minutes. If the amount of bacteria…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: 8. Solve the following equations for x (show all solutions for 0°≤ x ≤ 360°): (4) (a) 4sin(x-30°) -…

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Q: Determine the absolute extrema of the given function on the specified interval. Show your solution…

A: Please see the below picture for detailed solution.

Q: Evaluate fx cos² 2x² dx

A: Given: I=∫xcos22x2dx   ...1   As we know the common integral. ∫cosax+bdx=1asinax+b+C

Q: 6) How much isotope will be left after 80 years? A) 274 g B) 276 g C) 278 g 7) How long will it take…

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Q: Q21 A\ Are this function continuous f(x) x³-1 at xo = 1?

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Q: Find the linear approximation of the function f(x, y, z)=√√x² + y² + z² at (9, 6, 2) and use it to…

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Q: 1) (y ²-1) dx - 2y (²+x) dy 2) y² = x €²9-x² =C

A: See the details solution in below

Q: Find the sum of all rectangles shown in figure below in terms of x and y. x x/2 x/4 y/4 y/2 y

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Q: 9. For the polynomial function f(x)= x³ - bx² + cx-24 where b,cel, all of the following are…

A: The given function is a cubic polynomial: f(x)=x3-bx2+cx-24     , here b,c∈I If p is a zero of that…

Q: For Z= x²csc y,prove that Zxy is equal to Zyx

A: Given that,    z=x2csc y

Q: (4) 1. (4) 2. Find the equation of the line that passes through the points (6,8) and (2,20). Give…

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Q: [₁ In(x² + 4)dx

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Q: Evaluate fx cos² 2x² dx

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Q: 1. The expression log (at) is equivalent to: h logm a log t 1. A. B. log (at)" . log log Wat D. log…

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Q: Q5/Change the polar equation 2r = 2 + cos8.(2r - 1) to Cartesian equation

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Q: A stone is dropped into a still pond. Concentric circular ripples spread out and radius of disturbed…

A: Here we have to use the concept of the derivatives

Q: -10 h(x) -8 -6 f(x) x² -4 -9 k(x) x-3 2 10 1 8 00 2 -4 -6- -8- a(r)] 2 y = 2x+ ∞ X

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Q: Q2A. Find the volume generated by revolving the shaded area shown in the fig below about X-axis TO…

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Q: Let y = 3x² + 8x + 3. Find the differential dy when x = Find the differential dy when x = 2 and da 2…

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Q: = n²-7n +3 What is the 50th term of the sequence represented by n a n for n ≥ 1?

A: Given sequence, an=n2-7n+3 , n≥1

Q: Consider the initial value problem x' = 4x², x(0) = x0. For what value(s) of co will the solution…

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Q: Find the area of the shaded region. y=2x2+x-6 y=x2-4 W

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Q: Select the option that gives the vector product of i-2j and j + k. Select one: O 2i+j-k O -2i+j+k ○…

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Q: 5. Find the volume of the solid generated by revolving the area of a circle: (x - 2)² + y² = 4;…

A: In this question, we need to find the volume of solid generated by revolving the area of the given…

Q: Test the convergence and divergence of the following series, find the sum of convergent series. b)…

A: Given: Here, ∑n=1∞3n51-n=3∑n=1∞35n-1. and 3/5<1.

Q: Find S ³+1 ln ||+C In In | +C √²+1 None of the Above In||+C

A: We know, ∫dx/x= ln|x| ln|a| - ln|b|= ln|a/b| n*ln|a|=ln|an|

Q: Problem 11. Discuss the function f(x) = in terms of its concavity, inflection points, and local…

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Q: How much work is required to pump all the water over the top of a full cylindrical tank that is 2 m…

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Q: Part III. Evaluate the following. Justify each step if necessary. 1. If F(x)= [mm (8-) √²+3 dr. F'…

A: Let's solve diffrential of integration.

Q: (2x² - x - 1) x³ - x² ; 2 dx

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Q: D. Use double integration to find the area of the region R enclosed by the parabola y = 4-x² and the…

A: Let's find area by using double integration.

Q: 2. Find the sum of all rectangles shown in figure below in terms of x and y. X x/2 x/4 y/4 y/2

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Q: Using rectangles whose height is given by the value of the function at the midpoint of the…

A: Let's find area under the curve by using two rectangles.

Q: Determine the instantaneous rate of change of the function y = 5x + 2x² 1 with respect to x at x-4.…

A: Find instantaneous rate of change

Q: Let f(x) = 3 sin(x) + 2 cos(x). Find the following: 1. f'(x)= 3 cos(x) - 2 sin(x) 2. f'(5)-|

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Q: Determine whether lim cos F→0 exists, or not.

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Q: Additional Activities What function will you differentiate to get each function? 2. f(x) = 8x74x³ +…

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Q: 5. To obtain f¹(x) = -x +3+5, the domain of f(x) must be: A. x≤5 B. X25 C. x≤-3 D. x≥-3

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Evaluate: (answer in fractional form så S sinº x dx 0

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Q: For the function A whose graph is shown, state the following: y Wh -7 -3 0 a. lim A(x) X--7 b. lim…

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Q: 1000 I(t) = 1 +999e-.6t where t is in days and I represent the number of infected individuals. 1(t)…

A: It=10001+999e-0.6t…

Q: Find the derivative of the function f(x)=(sqrt(x-1)^2))/x^2+1)

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Q: 3) Suppose that in a certain fish hatchery, the fish population is modeled by the logistic growth…

A: This is a problem related to exponential model function. Based on the general formula and concept we…

Q: x-p In the table, Y, is defined by a rational function of the form p= Use the table to find the…

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Q: Additional Activities What function will you differentiate to get each function? 2. f(x) = 8x74x³ +…

A: Let differentiation of F(x) leads to the function f(x)=8x7-4x3+2x-3 So, F'(x)=f(x)=8x7-4x3+2x-3

Q: Q3) Use double integration to find the area of the shaded region between the y-axis and the curve x…

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Q: If air resistance is neglected, then the range R (in meters) of a projectile fired from a gun that…

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Q: Evaluate the following integral using trigonometric substitution. 36x² - 49 7 S² dx, x> 3 x³ 2 √36x²…

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