5. Fill in the blank: For x, y ER. Equality in the Triangle inequality is satisfied, i.e. Ix+yl = Ix| + lyl if and only if.

Q: dy Q4) Find for the following functions dx 1. y = 2x + e2x-1 2. y = sec x tan x 3. y = t2 + 2t t =…

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Q: Find the tangent equation for the function: f(x) = Vx2 +5 at x=2? Find the limits by using L.Hopital…

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Q: Find for the Implicit function dx x² – sin(xy) + y² = 5xy

A: Given

Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 4 1 lim t→+∞ \ 8t2 +9' 4t |(?, ?)

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Q: Find the area of the shaded region Blank 1 Note: Enter exact answer x = y 20 1000 y? 20

A: x=yx=1000y2Solve both the equationsy=1000y2y3=1000y=10The limits of y are from 10 to 20.

Q: Solve the following problems. 1. A thermometer reading 18°F is brought into a room where the…

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Q: 439) Use the matrix capabilities of a graphing utility to solvecif possible) the systems of linedr…

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Q: X – 1 limx → 1 V 4x – 2/x -

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Q: Q4) Find for the following functions (choose five only): dx 1. у %3D 2** + е2х-1 2. y = sec x tan x…

A: 1) y=2x2+e2x-1Differentiatey'=2x2ln(2).2x+2e2x-1dydx=2x2+1.xln(2)+2e2x-12)…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. F(x) = xe¬x²/128,…

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Q: the integral dx Va? – x? e may use x- educe the integral to a sine and dx= a cose de substitutions…

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Q: 2. Given f(x) = x' + ax² + bx has critical numbers at x=1 and x=3, find a and b. .2

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Q: 4. (x² – 4)dx c2

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Q: Evaluate the indefinite integral. x2 dx V0.2x3 + 2.7 + C

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Q: The discontinuities of the function f(x) =D 4x-9 are: x²-2x-15 Select one: O 5,3 -5, -3 -5,3 O 5,-3

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Q: 1 1. S dx х2-5х+6

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Q: Find the marginal profit function if cost and revenue are given by C(x) = 184 +0.3x and R(x) =…

A: This is a problem of differentiation . Based on the formula and concept we will answer the question.

Q: Question 7 Given that f (x) = 3x – 2 and ( x + 3 if x > 2 g(x) = Ja| - 3 ifr 2 what is (f + g) (-2)…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Ley y = tan x. (a) Find the differential dy. dy = (b) Evaluate dy and Ay if x = t/3 and dx = -0.1.…

A: (a) Here f(x)=y=tanxdy=f'(x)dxdy=sec2xdx    =sec2(π3)(-0.1)    =-0.4

Q: Evaluate the integral. HINT: [Use a shortcut.] e 8x - 1 dx

A: Using substitution ,

Q: 2.5 х2+3х-4

A: Given,  ∫ 5x2+3x-4dx

Q: Find the length of the spiraling polar curve 2e 40 From 0 to 27. The length is

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Q: Let C be the parametric curve defined by                         x(t) = t2 - 2;…

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Q: Find the area of the region enclosed by the curves y=x^2 and y=6x by integrating with respect to y.…

A: To find the area of the region enclosed between the two curves.

Q: Q2) Find the integral value for the following functions 3x 1. S 2. S(sec(4x) – 1)² dx 3. S dx V1+3x2…

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Q: Find the average value gave of the function g on the given interval. g(x) = 3x, [8, 64] gave =…

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Q: Find the exact length of the polar curve described by: r = 9e-0 5 on the interval -T <O<67. 6

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Q: 1. Find the particular solution using the Initial condition. xy'-y x.y(1) 7. Finally, sketch a slope…

A: Follow the procedure given below.

Q: c) Find a homogeneous differential equation whose general solution is given by y = c,x-1 cos 3lnx +…

A: Let's find.

Q: Determine the conjugate radical of the expression -8+35. O-8 -35 O NE + 35

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Q: Find the surface area when the curve C = {(x,y): 0 < x < 2, y² = 2 x} | about the x-axis.

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Q: dx 4. S; x2Vx2-1

A: Given: I=∫dxx2x2-1   ...1 As we know that; The trigonometric identities; 1). sec2x=tan2x+1 2).…

Q: Find the area of the region outside r = 5 + 5 sin 0 , but inside r = 15 sin 0.

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Q: d²y 2. Find the second derivative, dx2 a. x = t2 + 1 and y = t3 t2 + 2 and y = sin(t + 1) b. x = | 2

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Q: Solve for X in the equation, where -4 -3 A = and B = 5 3 -3 -2 -5 ABHTOMA RD 2X + ЗА 3 В

A: The given matrix,A=-4-3203-3 and B=0250-2-5

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Let i = and v =. If ü xi = then determine the value of 3A+B+C.

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Q: Q4) Find for the following functions dx 4. coth(ln x) y = 2x+3 3x+4 6. y = tan-1 V4x3 - 3

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Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (3t + 4)i + tj, 0 <t<1

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Q: Suppose we are given an integral of the form f f(g(x)) · g'(x) dx. We can transform this into…

A: The objective of the question is choose the correct option.

Q: Find the limit. lim (t i - 7 j+ t k) t-5 lim (t i - 7 j+? k) i+ i j+ i k

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Q: dy Find dx of æ³ – y? = 5 by implicit - differentiation and evaluate the derivative at this point:…

A: According to our guidelines, we can answer only one question or three subparts of a question, other…

Q: dy Q4) Find for the following functions dx 1. y = 2x + e2x-1 2. y = sec x tan x 3. y = t² + 2t t =…

A: Given

Q: A ball is shot from the ground straight up into the air with initial velocity of 49 ft/sec. Assuming…

A: Let's find.

Q: Verify Green's Theorem by evaluating both integrals aN y? dx + x² dy = /, J da ay ax for the given…

A: We have to verify the green theorem for the

Q: 1. a) Find the linear approximation of f(x) = Vx at x= 27 %3D b) Use it to approximate V26.9

A: To find linear approximation of given function

Q: Find the smallest value of x for which the series Σ (x+101)" 2ln(n) n=2 is conditionally convergent.

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Q: The graph of the function f is shown below. If lim exists and f is not continuous at a, then a…

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Q: Find Inz3 dz

A: LetI=∫lnz3zdzLet z3=udifferentiate 3z2dz=duDivide 3z2 on both sidedz=du3z2dz=du3z2Divide z oboth…