Q.1- Evaluate the following integrals (answer two only) a- So √x e-√x dx 1

Q: For a battery of voltage V and internal resistance r, the total power delivered to a load with…

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Q: Find the value of the Sum Σxi' if x₁ = 8₁ x₂ = −3₁ X3 = 4₁x₁4 = - 1=1

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Q: c - [² x ² (1 - √x ) ³dx 0

A: In this question we have to evaluate the Integral.

Q: Question 12 If A is the area of a variable square with side s, what is the rate of change of A with…

A: Solution ) area of variable square A = s2  Differentiate with respect to s  dA/ds = 2s [ formula…

Q: An isosceles triangle is inscribed in a circle of radius R. Find the value of 0 that maximizes the…

A: In this question we have to find which option is good.

Q: ind the given inverse Laplace transform. 1 (7.3.20 s² +65 +10 a. e-³tsin(t) 5. e³tsin(t) C.…

A: Finding the inverse Laplace

Q: x³dx S 17. √(1-x²

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Q: I Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: 2. Differentiate. a)/(x)=12x¹ 5 -1 √√2-1 c) h(x)=- b) y = - 3x² 2x+3 - d) y = 21+1 31-2)

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Q: Use the formula for the binomial series: (1 + x) = 1 + mx + 1 + 2 =1 100 = o obtain the Maclaurin…

A: See the details solution in below

Q: The half-life of chemical substance is approximately 9 years. Initially there is 80 grams of the…

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Q: If f'(a)=, what is the slope of the line tangent to the graph of y = f(x) at the point (a, f(a))? O…

A: Given: the curve, y=fx.f'a=12

Q: Find the volume of the solids generated by revolving the region bounded by the curves y = 7r² and y…

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Q: A teenager is selecting which options they would like for their ice cream treat from the list below.…

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Q: b. Find the values of dz/8x and dz/dy for the following expression: xe+ ye² + 2 lnx - 2 - 3 ln 2 =…

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Q: 2 3 1. Determine the derivative to y² = x³ + y² + 2xy

A: Given problem:- Determine the derivative to y2 = x3 + y3 + 2xy

Q: 1.y = 5x + 2

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Q: Evaluate the integral.   The integral from 1 to 4 of e^(4/x)/x^2dx

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Q: In general, the sketching of the trace of any function can be facilitated by dividing the plot area…

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Q: 8. The polynomials x - 1, (x - 1)2, and (x - 1)³ span R3[r]. 9. If S and T are finite spanning sets…

A: Given

Q: f(x) = 5x + 2

A: Given.

Q: Solve the differential equation. 2. (y^2-2xy + 6x) dx – (x^2 – 2xy + 2) dy = 0

A: To solve the given diffrential equation.y2-2xy+6x dx-x2-2xy+2 dy=0

Q: Find A-B using the following matrices: 5 6 1 2 9 3 A-3 5 8 B = 4 0 3 4 6 7 -5 -1 3

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Q: Given that lim f(x) = 9 lim g(x) = -2 lim_h(x) = 0, X→3 X→3 X-3 find the limits, if they exist. (If…

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Q: Find given that cot (3x-2y)=2x-3y. dy da

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Q: lim x-1 2x³ +3 3x² + 1 - 3x + 2

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Q: (1) 2. Determine the total number of different outfits you can create from your closet if you have…

A: This is a problem related to permutation and combination. Based on the general formula and concept…

Q: Consider the initial-value problem y' + exy = f(x), y(0) = 1. Express the solution of the IVP for x…

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Q: A cube is box all of whose sides have equal lengths 3s². True False

A: a cube is made of 6 squares whose sides are of equal length

Q: 3 2 3 0 Given the matrices A = B = 3 -1 5 for the matrix X in the equation XA + 3B = C. and C Го…

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Q: 6X-1 4X+1 X+7<6X=1 6 OX<-89/2 (-∞, - 89/2) OX<-89 (∞, -89) OX<-2/89 (-∞, -2/89) OX<∞ (89/2, ∞)…

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Q: Which of the following relations is not a function? a.{(3,3),(2,3),(0,4),(1,4)} b.…

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Q: Use Lagrange multipliers z = f(x, y) = x² - xy + y² to find the absolute maximum and minimum values…

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Q: Ⓒ Differenitale y = √3x-7 X

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Q: If f(x) = -1/2 then f(³)(x) = , A O 2 2:3 O O 6 2 ການ 6 x4

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Q: For second-order differential equations that cannot be solved by algebraic methods, the…

A: For second order differential equations that cannot be solved be algebraic methods, the leibniz -…

Q: Find the area of the region enclosed by the curves y = x + 5, y² = = x, y = −1, and y = 2.

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Q: What is general solution of the given ODE. * dy = cos² (x − y + 1) dx cot (x-y+1) + x + 1 = C Option…

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Q: The following logarithmic expression, log2 (4), when completely simplified becomes

A: Given,  log2(4)x

Q: Problem 6. Find the equation of the tangent line to the curve x²y-ay² = -6 when z = 2.

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Q: Given z = 7t - 43 and y = 49 sin t dy (i) de to (ii) (1₂)

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Q: Evaluate the fsinz integrais belovo sin² xcsc 2x dx

A: Evaluate the integral

Q: 4. Classify the following differential equations according to whether they are linear or nonlinear.…

A: For (A), The above differential equation is linear. For (B), It is the same as dydt+1=0. So, the…

Q: Determine the equation of the line that is tangent to y = 2 tan x, where x = 4. O-4x + y - (2-) = 0…

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Q: 2. (3x² - 2x + 1)dx Step 1: Find F(x) by integrating the function Step 2: Apply FTOC Step 3:…

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Q: f(x) = (2x - 3, if x = 2 # 3, if x = 2 12x 3,1

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Q: Q5: Find the inverse Laplace transform of: f(s) = 3²(²-3)

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Q: Find the area bounded by f(x)=x2-3x + 7 and g(x) = 2x + 7. (Round answer to two decimal places.) O…

A: Given equations, y=x2-3x+7y=2x+7We need to find point of intersectionx2-3x+7=2x+7x2-5x=0x(x-5)=0x=0…

Q: calculate the purchasing power of this amount

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Q: Obtain the orthogonal trajectories of y=Cx^2 and compute for the positive value of y of the…

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