III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = x – 3x? + 4x – 12 2. y = (x? – 3)?

Q: Which of the following integral can be used to find the volume of a solid on the first octant bounde...

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Q: Evaluate: tan( 4x- -In |cos (4x + 3)|+C B -In |sin(4x + 3)|+C -In |cse (4x + 3)|+C -In \sec (4x + 3)...

A: the given integral,        ∫tan(4x+3) dx

Q: x3-/(x) 2. Let f be defined by the equation f(x) = V3- x. a. Evaluate lim f(x) x-3+ b. Evaluate lim ...

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Q: Which of the following integrals will yield an inverse trigonometric function? e2x dx 4+e2x wdw (B 2...

A: Let I=∫19-16x2dxI=∫11-16x29dxI=∫112-43x2dxWe know tha ∫1a2-x2dx=sin-1xa+CThereoreI=sin-143x1+CI=sin-...

Q: A. Fill in the tables and guess the value of the limit. 1. lim f(x), where f(x) = х3 — 1 x2 -1 %3D f...

A: Given that        f(x) = (x3 - 1)/(x2 - 1)  Here we have to find            limx-->1 f(x) .

Q: csc2tdt=In|csc2t – cot21|+C A) True B False

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Q: Use the difference an+1 – an to show that the sequence - {n – 7"}, +00 is strictly increasing or str...

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Q: Solve the differential equation (xy² + x – 2y + 3)dx + (x²y – 2x – 2y)dy = 0 -

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Q: evF dr + A в 2 2 E) None

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Q: Solve (x² + 4) y' = 2xy %3D

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Q: Set-up the integral to calculate the area of a region bounded by х-у-3 and y-x2 -6x+9? A dy dx x2— б...

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Q: The graphs of the functions f and g are shown in the figure. y 4 f 1 -1 1 2 3 4 6. f(x) Let u(x) = f...

A: topic - functions and derivatives

Q: The integral csc(0.5) dx is equal to Sco A None of the given choices B 4tan¬le0.5x + C © 21n|csc(0.5...

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Q: having

A: We will find the half life. 

Q: I Solve the di fferential equations ( 2x-5y+12) dx +(7x-4y+15) dy - o 2.

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Q: E. DIFFERENTIATION Obtain the derivative of the following functions: (2x³-1)5 y = (5-3x)*

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Q: Calculate the volume of a solid on the first octant and under the plane defined by 2x+5y+7z=46. Roun...

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Q: If f(x)dx=cot x² +C , then f (x) is equal to A -2cscx? B -2xcsc?x? © In/cscx²| D O In/sinx²|

A: We have to choose correct option for value of f(x)

Q: 18. If x? + 2xy = y? then y' is x+y b. 2x + 2y a. y-x d. -x C. y 19. Evaluate S(3VE+ dx a. 2x + 4 V ...

A: I am attaching image so that you understand each and every step.

Q: P. Iff: [-4,0]→R is defined by e* + sin x, its even extension to [- 4, 4] is given by (a) – e-lx| - ...

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Q: 7 1. f(x) = 6 {/x? – 20 {x* + 4 find f (4) (x).

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Q: Solve the differential equations x (x- y²- x)dx =y(x²-y²) dy when x=2, %3D y=0

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Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the...

A: Topic = Derivative

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper f...

A: Use geometric series test to solve given problem.

Q: In 3 [te' i + e'j + In tk] dt 1

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Q: sinx 3. f(x)=(x)'

A: Given: f(x)=xsin xTo find the first derivative of the given function Formula: (uv)'=uv'+vu'ddx(sinx)...

Q: - In y = e' sin x

A: We have to find dy/dx of the above equation.

Q: sin³ydy 1+cosy

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Q: y= fx) y-g(x) Use the graphs of f and g in the accompanying figure to find the limits that exist. If...

A: A) limx→2 [f(x) + g(x)]=limx→2 f(x) +limx→2 g(x)=1 + 0(f(x) is not defined at x=2 but ,limit is 1 at...

Q: Solve the diff eq (ху?+x-2у+3)dx +(x?у — 2х - 2у)dy %3D0

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Q: 1. The flow rate of a fluid is described by F in units of kg/(m²-s). It is flowing through a membran...

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Q: Calculate the volume of a solid on the first octant and under the plane defined by 2x+5y+7z=46. Roun...

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Q: Homogeneous Differential Equation: (r* +2xy– 4y° kdx– (x² – 8.xy – 4y dy = 0 Let: x = wy dx= wdy+ydw...

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Q: Vil 12 sin (x) cos' (x)dx by using walli's formula. 27. a is equal to? A.1 B.O C.1/10 D.pi/2 The def...

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Q: Find the differential equation of the family plane curves described. Draw atleast three members of t...

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Q: Given that lim f(x) = 2, lim g(x) = – 4, lim h(x) = 7 find the limits. Enter the exact answers. (a) ...

A: As per our guidelines we are supposed to answer only first three parts.kindly repost others parts as...

Q: Find the Maclaurin Series of tan-(x2) at x = 0.25

A: First we find Maclaurin series of taninverse x then replace x by x2 

Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the oute...

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Q: In each graph, a parent function has undergone a transformation of the form f(kx). Determine the equ...

A: We need to find the equation of transformed graph red using the graph of parent function green.

Q: Which of the following integral will give the volume of a solid generated when the area bounded by y...

A: This question is related to definite integration, we will solve it using given information .

Q: Using the substitution y = vx and dy = v dx+ x dv, the differential equation with homogeneous coeffi...

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Q: etermine each function's domain and range. If applicable, use a graphing utility to confirm the hand...

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Q: If the infinite curve y = eSX, x > 0, is rotated about the x-axis, find the area of the resulting su...

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Q: evF dr S-

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Q: The quantity of charge Q in coulombs (C) that has passed through a point in a wire up to time t (mea...

A: we have given Q 

Q: 16. Evaluate S x² cos(x³) dx a.) -sin(x³) + C b.) sin(x') + C c.) - sin(x³) + C d.) sin(x') + C

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Q: 1. d'y_dy - 42 + y =r²-2t +3 dr dt 2. y"-7y'=(2x-1)sin 2x 3. y'-5y=xe" – xe*

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Q: Suppose that f(z, y) = x°y?. Find the directional derivative of f(x, y) in the directional (1, – 1) ...

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Q: Examples: Find the limits of the following: 4. lim tanx tan"(-0) = - 2 5. lim secx = lim cos (-) = c...

A: Given:   Limit Equations is given

Q: Find the general solution of y"- 10y'+ 25y - 0 Oy= Ce- + C2ze* Oy - Ce + Cwela Oy- Ce a + C,ze be Oy...

A: Given,y'' -10 y' + 25y = 0     .......1this is homogeneous equation.Since,y" = D2yy'=DySo putting in...