Q1): Prove that: A square matrix B has inverse if and only determinant of B is not equal zero.

Q: Jmin = ymax =

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Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: (-3, 3) & (0, 0) Y₁ = X₁ = ; X₂ = Trend: m = 3 Y₂ = Final answer:

A: Solving the problem by finding the slope and trend.

Q: Find the interval of convergence of the series xn Σ n8" n=1

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Q: Find the Laplace Transform

A: Topic:- application of integration

Q: 1) lim x + 5 X 1.5 2 2.5 2.75 2.99 F(x) X 4.5 4 3.5 3.1 3.01 F(x)

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Q: A hot air balloon rising vertically is tracked by an observer located 3 km from the lift-off point.…

A: topic - trigonometric ratios and application of derivatives

Q: Syy-mat sama dy ³

A: Follow the procedure given below.

Q: Find the volume of the solid generated by the revolving Shaded about region the 7-axis 1 0.5 X =…

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Q: A rectangular swimming pool is 42 ft wide by 75 ft long. The table gives depths (d) from x = 0 at…

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Q: (a) Find the general solution of the differential equation d²y dx² +9y = x² + x + 1.

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Q: Find the area of the shaded region. 49- y=49-x² 35- 21- 7- اتنا -17-1 -21- -35- -49- F3 5 th Fo Q Q…

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Q: Numbers 13,14,15 please

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Q: (CLO-3] The second derivative f(x) of a function is given. Use this information to find all values…

A: The second derivative f''x of a function is given. By using this information to find all values of x…

Q: Given R(t) = 4 costi + (1+ 3cost)j +5sintk. Find T(t). T(t) = -sin ti -sintj + costk Option 1 3 4 5…

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Q: 1. Determine the radius of convergence of the series 1 + x/2 + x²/3 + x³/4 +...

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: what is b if ( log b x) ' = 1/3x

A: Concept: Derivative of log(x) is  logx' logx'=1xln(10)....................(as log is default base…

Q: η3+n2 (5) Σ=o (n+1)!

A: Series ∑n=0∞ n3+n2n+1!

Q: Question 11 (CLO-2) Evaluate lim f(x) where (3x-4 if x2 02 O does not exist O 10

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Q: Consider the functions z = 7 e* In y, x = In (u cos v), and y = u sin v. ex əz dz (a) Express and as…

A: This question can be solved by the concept of partial derivatives.

Q: Use linear approximation, i.e. the tangent line, to approximate √25.2 as follows: Let f(x)=√x. Find…

A: Linear approximation for fx=x at a=25The linear approximation of the function fx at point a is Lx =…

Q: Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 62² and…

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Q: center of the mass of a thin density covering the Constant density 8. by the x-axis and EA Y = 3/2/…

A: We have been given that curve  y =32cosx with -π3 ≤x≤π3                  and   density…

Q: Find the largest triangle that can be inscribed in the ellipse (x2/a2)+(y2/b2)=1 (assume the…

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Q: Additional Activities (-2.39) a 4 88/88 20 10 10 -20 30 40 1 (2.7 Solve the following problems. A.…

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Q: The half life of a decaying substance is the amount of time it takes for the substance to reduced to…

A: Let us assume it takes n half-lifes to reach 10mg

Q: SORRY {CLO-1} Determine the horizontal asymptotes of the given graph. +8fx₁ 4 12-10 Oy=2 colorwa…

A: In given graph  ,it is easy to find a horizontal asymptote by visual inspection. Observe by starting…

Q: Find the extrema of each given function on a specified closed interval. 1.) g (x)= x³ - (3/2)x²,…

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Q: Əw at = xysin(z2), x= s-t, y=s2, z t². Use the Chain Rule to find .

A: We know that derivatives of d(xn)/dx = nxn-1. And d(sinx)/dx = cosx  Here i attached the solution of…

Q: Given z *- Find Z*** www.xy. www Option 1 Zxx = -2x³ Zxx = -2x-3 Option 3 Zxx = 2x 3 Option 2 none…

A: Given

Q: Evaluate lim f(x) where X-3 (3x-2 if x3 09 O does not exist O 11 07

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Q: Q3/Find the value of x If the approximation of the integral ſ f(x) dx by trapezoidal method is given…

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Q: (c) 1 e¹/x x² dx

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Q: Əw Given w = xysin(z²), x=s-t, y=s², z t². Find Əy əw ду = y sin z ² Option 1 O Option 3 aw = x sin…

A: Topic:- derivatives

Q: 51 1. A parabola with directrix y = == 32 and one endpoint of the latus rectum at nat (-²,-2)

A:

Q: Find the value of the following implicit derivative tan y-sec x=5 find...y'

A: Given problem :- Find the value of the following implicit derivative   tan(y)-sec(x) = 5 find   y'

Q: Given R(t) = 4 costi + (1+3cost)j +5sintk. Find || R'(t)||. 5 O 4 O 2 O none of the above

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Q: 1. IF PLx) =5х4 Sox2+9х2 Find F'(x) and F'(2)

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Q: [CLO-2] Evaluate the Indefinite integral by using the substitution rule. S√tan (x) sec²(x) dx…

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Q: 2. Write the given (total) area as an integral. a. The area above the x-axis and below y = 4 - x² b.…

A: Let's find  area between given curve and x axis.

Q: he point  P(8, −3)  lies on the curve  y = 3/(7 − x). (a) If Q is the point  (x, 3/(7 − x)),  use…

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Q: Write an equation for a rational function with: Vertical asymptotes at x = 6 and x = -4 x intercepts…

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Q: Particular solution of y" - 5y'=x-2, when x = 0, y = 0, y = 2

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Q: 4η-3 (3) Σ=c 2=0 2η5

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Q: Find the radius of convergence for the series 3 n³ xn 3n OR=3 O O OR= 8 n=1 R = R= - الله R = 1 8

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Q: X1 (-1, 2) & (-3,0) Y₁ ; X₂ = m m 11 -C Y2 =

A: Solution of given question is written in below steps.

Q: Question 18 (CLO-2) Find all vertical asymptotes of f(x). 4x f(x)=64-x Determine whether f(x) or…

A: This is a problem related to vertical asymptote calculation. Please find the procedure given below.

Q: [CLO-2] Evaluate the improper integral. 8 √₁² (0-²x + ₁ 72² 2² ) ₁ dx 1 1+x²

A: Follow the procedure given below.

Q: 2 3s +9 Option 3 23 -e³t e-3t Option 4 None of the choices Option 2 Option 1 2 -3t 3 3 N|W 2 co

A: As we know the inverse Laplace transform identity; L-11s-a=eat   Given: Fs=23s+9

Q: Evaluate the following integrals: O • (Cartesian to Polar) Civen the cartesian coordinate, find of…

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