| 1) 2Ln(√x + 3) + 2Ln(√x − 1) = Ln(6x - 7) 2)3x+2 = 27

Q: H.W: Given the following table find x3, fo Af₁,Af₂, A² fo j xj Afo A² fo 0 fo 30 A² fo 4 20 Af₁ 2 14…

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Q: Find the critical values (if any) of the given functions. With solution please.

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Q: - Investigate if the integral is convergent or not. Justify your answer.

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Q: 4. A triangle has sides of length 13 cm and 22 cm and has an area of 100 cm² a) Use Heron's formula…

A: We have to solve the side and angle of given triangle.

Q: 1 f(x) = (x² + 3x)² at [2,3]

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Q: Evaluate the integral. "π/4 J.T tan (0) sec²(0) de

A: This question can be solved using integration by substitution.

Q: (c) Use the WASHER METHOD to set up a (sum of) definite integral(s) that is equal to the volume of…

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Q: V.P. [ -8 COS X (a²-x²) -dx, (a> 0).

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Q: 1)y=(8+7x³) Find the derivative of the following functions 2)y = (x +5)*(2x + 3) 3)y=√(x²+3)²

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Q: Let f(x) = 2x² -5x - 7. Expand and simplify: f(x +h)-f(x) h =

A: The answer is given below:

Q: Convert the angle 270° to radians. Give the exact value and use pi for .

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Q: State the order of the given ordinary differential equation. (1-x)y" - 4xy' + 7y = cos x Determine…

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Q: k 1. Find the value of in a. 0.298597 C. 0.498597 2. Find the value of a. 0.138629 c. 0.158629 k in…

A: Solution

Q: Consider a plate (the plate has the same shape as the region enclosed by y = x² and y = 4) submerged…

A: Let's find force(F).

Q: Find the area of the region enclosed by the curves y=2 sin x y = 2 sin x and y=2 sin 2x for 0≤x≤ T.…

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Q: Find the value(s) of k that makes the given function continuous. (-x+2 if x < k f(x) = 4x + 3 if k ≤…

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Q: 1) e5Ln x+4Lny-Ln z 2) 2Ln√x + 2Lnez - 2Lne* Rewrite the following quantities

A: Given :1. e5Lnx+4Lny-Lnz2. 2Lnx+2Lnex-2Lnex

Q: Solve cos(x) = - 0.38 on 0 < x < 2π

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Q: 3. A right circular cone has the following dimensions: Radius: R Height: H Then its volume is R²H.…

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Q: Show that: le a (i) a е a а al (2a +1)(1-a)2

A: Given :laaalaaal=2a+ll-a2

Q: Find the number in the interval [0,3] such that the difference of its square from its cube is the…

A: Given problem:- Find the number in the interval [0, 2/3] such that the difference of its square from…

Q: Question 4. A lamina with the density p(x, y) = x² is bounded by the curves y = 3x² and y=x² +2. 1)…

A: Let's find mass of lamina.

Q: Find the derivative: y = ln (3x + 1) O y = O y = Oj = 2 y = = 2ln(3 + 1) (3x + 1) 6 (3x + 1) 3 (3æ +…

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Q: Differentiate the function with respect to the independent variable. x f(x) = 4x cos+ + cos f'(x) =…

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Q: 2. Find using implicit differentiation. Enclose final answers. dx (a) 4x³y² + x¹y³ = x + y = 0 (b) x…

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Q: T/6 6 tan 2x dx

A: In this question, we need to evaluate the given integral.

Q: (*). (1) without a calculator. We will do the followings: 1.2.3.4 7.6.5.4 = 2.3.4 7.6.5 7.5 = 1 I…

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Q: Which of the following functions is entire? For each, justify. = 2(32) ƒ(z) = 2'

A: Given :   f(x)=2(3z)

Q: For the function whose graph is shown below, at which value of x is the graph continuous and…

A: We know  Function differentiable if it is continuous through out its domain   At sharp/corner points…

Q: How to find a and b for a triangle when I only know that c is 15? (using the pythagorean theorem)

A: Concept: Pythagoras theorem: It states that the addition of the squares of the perpendicular and…

Q: . The region is bounded by X = y² and x = 4(y − 2)² Using horizontal rectangles, set – up the…

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Q: Find f(t). ℒ−1{9s / (s - 4)2}

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Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

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Q: Find f'(x) where f(x) = x. 2? O f'(x) = 2 (1+x. ln2) O f'(x) = -2 (1+x. ln2) ○ f'(x) = 2 (1-x. In2)…

A: Given :f(x)=x.2x

Q: Prove the limit below exists and find its value to 6 digits but replacing n for a large value and…

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Q: The function f(x) 2x³ = local minimum and one local maximum. This function has a local minimum at x…

A: The given function:fx=2x3-45x2+300x+6.We need to find its local minimum and local maximum.

Q: = f(x,y) = x² Determine whether the function z = (why or why not) +y + y² for for (x, y) = (0,0) (x,…

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Q: Find the acceleration u= 2x² + 3y, v=- - 2xy + 3y² + 3zy, Example the following flow field: W =- at…

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Q: Solve for the volume of the solid generated by revolving about the y-axis the area under y x = 4 to…

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Q: 31. The function fƒ: R→ R is defined by f(x) = (a) Show that f is a bijection. (b) Determine f¹(x) x…

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Q: Find y': COS X y = 1-sin x O y' = sin² -sin x-cos² x (1-sin x)²

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Q: Find the derivative of the function f(x) = = sin(x) - 1 cos(2x) + 1 4

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Q: A spherical balloon is inflated with gas at a rate of 800 cubic centimeters per minute. (a) Find the…

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Q: Investigate if the integral is convergent or not. Justify your answer.

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Q: Consider the following. [u-5(6 - u³ +4²0) du Simplify the integrand by distributing u¯5 to each…

A: We know that integration power rule is given as - Integration of xn is xn+1/n+1 +C ; here C is…

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 16 dx +8

A: We have to find the integral

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: 3) (11x + 17) dx 2x² + 7x - 4 S

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Q: 2x² + y² +3z² = 1 y² = 4x x² -z² = y 2z = x² +4y² 2x + y − z =1 z = 4y²-x² E

A: We have to match the graph with equation and write name of these shapes.

Q: Given: y = = 4 cot (3 - 2x) Find: dy dx 0-8 csc² (32x) O csc² (3-2x) 08 csc² (3-2x) -4 csc² (3-2x)

A: Given y=4cot(3-2x)To find dydx: