Direction: Translate the following notations into statements in terms of the area under the curve. 1. 2dx = -2 2. (x + 5)dx = –- 13 2 3 3. xdx = - -

Q: Using the method of LaPlace Transform, solve the following IVPs a.) y" + 8y' + 25y = 13e-2t…

A: As per bartleby guidelines we only give first question answers because questions are lengthy.

Q: Find S 2t²e*dt

A: Given query is to find the value of the integral.

Q: The point P(48, –14) is on the terminal side of angle e in standard position. What is the value of…

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Q: General solution of x dy = (2xex – y + 6x2) dx %3D

A: The given equation is: x dy=(2xex-y+6x2)dx That can be written as:…

Q: g³ + x² + 2x+1 d.x (x² + 1)(x² + 2)

A: Explanation of the answer is as follows

Q: Find the first partial derivative of fx , fy and fz of f ( x , y, z ) = 2xyz +  tan x  +  y sin z…

A: Given problem:- Find the first partial derivative of fx , fy and fz of f ( x , y, z ) = 2xyz + tan x…

Q: Assignment On Integral of Exponential & Logarit Determine the integral of the ff. functions. 1. S -…

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Q: 9. The general solution of y" + y = cos? x

A: Given :   y"+y=cos2x

Q: Consider an angle in standard position with measure - 1615°, in which quadrant does its terminal…

A: given angle θ=-1615°

Q: Given the vectors v and u, answer a. through d. below. v= 10i + 2j – 11k u=7i+24j a. Find the dot…

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Q: (21) Let y be a function of r. Find y'(x). Leave your answers unsimplified. (a) y =…

A: Differentiate wrt x

Q: Given the function h(x)=*-4 and k(x)=-+4. 9. 3 а) State the domain of h(x) and k(x). b) Find and…

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Q: Evaluate the given integrals. 1. cos 2x dx

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: dx V(z – 2)° – 11 Vxt-2)* - || x - 2 du 1 (steps) da = /11 du: V1I u = x-2 du = dx Substitute u =…

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Q: x*- 2x³+x² xdx

A: ∫x4-2x3+x2xdx ∫x2x2-2x+1dx ∫x2(x-1)2dx ∫x2(x-1)dx ∫ x3 -x2dx x4/4 -x3/3 +c

Q: A ladder of length 15 meters is leaning against the side of a building. The foot of the ladder is…

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Q: Write an equation for a rational function with: Vertical asymptotes at x = 3 and x = 1 x intercepts…

A: We have to find the function

Q: Find the general solution of cos x dy + (y sin x – 1) dx = 0

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Q: Find the first derivative of y = cos4 x – sin4 x and y = x3   –  x2 cos x  +  2x sin x  + 2 cos x…

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Q: The general solution of (D²+2D+1)(D²+4)y=0 @ -+Ceª A y=(C,+Cx)e*+C;e B none of the given choices ©…

A: We have to find out the solutions

Q: . Evaluate the following: (ey)dy dx A. e -1 2. В e-1 С. 2е +7 D.

A: Given query is to fins the value of the integral.

Q: 11. Given the functions: g(x) =In(4 – x) and h(x) = 4 – x² find and simplify the following: (a) h(x…

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Q: 14. Re-write the equation f (x) = x² – 10x + 16 in vertex form. Note: the author of your textbook…

A: Given:      fx=x2-10x+16   Set the polynomial equal to y to find the properties of parabola.…

Q: 1. Find the area bounded by the curves y?=2ax, y²=4ax-a? 2. By integration, show that the area of a…

A: As you have asked multiple questions so I have answered first question as per the guidelines

Q: x2 (x+2)³ In Ix + 21 + 4x+6 4x+6 (x+2)= In |x + 2| – (x+2)= +C Option 1 Option 2 ihk+ 21- 4x+6 In lx…

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Q: 3. X Cos X dx COS

A: On solving this we will get

Q: Is the function continuous on the interval 0, 27? 1+(sin z)? O yes O no cannot be determined

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Q: What is the slope of the tangent line to the curve a +y +¢y=3 at the point (1, 1)? O -1 O 1 cannot…

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Q: Describe the transformations of the graph of y=vx to obtain the graphs of the following functions.…

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Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

A: We want to find relative maximum, minimum and saddle points.

Q: find the derivatives of the following with complete solution a. y = sec 2x b. y = sin x -

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Q: x + 4 dx x² + 2x + 5

A: Given ∫x+4x2+2x+5dxTo evaluate the integral:

Q: cos (0) + sec (-0) tan(0)sin (20) 5. Simplify the following expression:

A: Simplify the following expression

Q: Cansider the Relmann sum for (x) = x+ 3x over the Interval [0, 8] (see figure), where *. =0, , = 1,…

A: Consider the Reimann sum for fx=x2+3x over the interval 0, 8 shown in the figure, where x0=0, x1=1,…

Q: he velocity function is v(t)=−t2+4t−3 for a particle moving along a line. Find the displacement and…

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Q: Moshe has 100 shares in the company that manufactures the coffee machines. The current market price…

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Q: ydy J-7-By-y

A: Given problem:- ∫ ydy/√(-7-8y-y2)

Q: 2х + 1 (х — 2)(х — 3)2

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Q: Use the specified substitution to find or evaluate the Integral. (Use C for the constant of…

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Q: What is the derivative of sin(2x) at the point (0,0)? O 2 O -2 O 4

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Q: wa?y+ xy² + tan (wx) Determine dyðwdx Your answer

A: solution

Q: Sove a lake, sere hft) represents the height above the water, in feet, at t seconds. a) Determine…

A: Topic:- application of derivatives

Q: 19. For the following function f (x) 3x-4 %3D find any x-intercepts, y-intercepts, and equations of…

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Q: 1. If sin 0 =, and 0 is in QI, find sec 0. 2. Given cos e = .e is in QIV, find csc 0. 3

A: We have to find out the trigonometric ratios

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, C = 6 (x – 6)²…

A: We have to find out the polynomial

Q: 13п What is the exact value of sin-(x) if x =cot 4 A 4 B 4 D 티2

A: Option (c) π2

Q: Use linear approximation to approximate e.03 О 1.03

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Q: (-1)" Vn

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Q: Find the first derivative of y = ( ex – e –x ) /  (ex  + e –x ) and y = ln [ x  +  √ (x2  + 1) ]…

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Q: Using the method of undetermined coefficients, what is the modified form for a particular solution y…

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