Q1. Each of the following curves cuts out regions above and below the x-axis between the given points (see Lecture 8.2). Find the total area enclosed by each curve and the x-axis between the given points. (i) f(x) = x – 9x2 + 18x between r 0 and r = 6. (ii) f(x) = 3 cos(x) between r = - and r = %3D %3D -

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A: I have stated the used formulas in the solution.

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Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: 2. Let R = {(1, b) ERX R: there is an integer k such that a – b = 2kn}. Prove that R is an equivalen...

A: us the definition of reflexive , symmetric and transitive property of relation to prove it is equiva...

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Q: Question 1 For each improper integral below, show that it diverges or find its value. (a) | Va In z ...

A: in multiple question we are allowed to answer only first three sub parts of question.

Q: — 4т + 10у — 6 2 — 5у — 3

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Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

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A: Given query is to find the average temperature of the coffee in the first 40 min.

Q: 14. Evaluate the following limits. (3-x+x2, 5x+1Y e) lim 2x y-0+ 5x-7 lim 2 f) X0o ( 3x2 x sin x lim...

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Q: 3 da IV9z2-4 o+ (z등) o 음sec-l (금) + C ○ 을sin-1 (을피) + C 0 3sin-1 (을2) +C O 3 sec -1. (을띠) + C

A: This question is based on indefinite integral.

Q: If a cup of coffee has temperature 100°C in a room where the ambient air temperature is 20°C, then, ...

A: Solve for average temperature after 40 min. 

Q: 1. Let R be a relation on the set A = {1,2,3,4,5,6,7,8} defined by aRb if and only if 2a/b?. That is...

A: Range of R = {y: x,y∈R}. Inverse Relation : R-1 ={y,x: x,y∈R}.

Q: Use finite approximations to estimate the graph of f(x) =x between x = 0and x = 1 using 1. a lower s...

A: Let's find. 

Q: 4.) Find dy/dx. Given: 5x - x'y' = 2y %3D 5.) Find dy/dx. Given: y? + 2xy² – 3x + 1 = 0 | 6.) Find d...

A: 4. 5x-x2y3=2y5. y2+2xy2-3x+1=06.1x+1y=1

Q: use Substitution method to Schve (3メ -2Y +1)dx -(X-2Y-3)dy=o

A: Given:   3x-2y+1dx-x-2y-3dy=0

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A: A relation R from A to B is a function if each value of A is mapped to only one value of B.

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Q: 2. x cosh x? sinh x2 dx

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Q: Use logarithmic differentiation to find the derivative of the function y = 7x"(#), where r (x) = 8x ...

A: Logarithmic differentiation means taking logaritm first then take derivativea(x)=b(x)c(x) then for d...

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Q: 12. Solve the following inequalities. a) -7x + 8 < 4x - 2 b) (3- 4x)(x + 1)(7 – 2x) <0 6x-9 c) 3x-2 ...

A: For (a),     -7x+8≤ 4x-2⇒-7x≤ 4x-10⇒-11x≤ -10⇒x≥1011 For (b),     3-4xx+17-2x≤ 0⇒x≤ -1  or  34≤ x≤72

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A: Given: So, here an=1317n-1. Now,                limx→∞ 1317x-1=13·limx→∞ 117x-1=13·limx→∞ 1limx→∞ 1...

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A: We have to find integral value in place of box And volume. Of solid torus. 

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A: Given  :initial No=5000 gramsR(t)=No12t25limt→175R(t)

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Q: 26. Find the area of the region bounded by the curve y = 4x – x?, the lines x = 1 and x = 3 and the ...

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A: ∫15cos(x)xdx ; n=5

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Q: ·를 sin' X V cos x

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

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Q: Find the area of the shaded region. y y= v x 1 1, 1) X= 27 1 y = 10 15 20 25 2. 4.

A: Given query is to find the area of the shaded region.

Q: 27 Given Cost and Revenue functions C(q) = q° - 10q +56q + 5000 and R(q) = - 3q + 2600q, what is the...

A: Let's find. 

Q: The function f is shown below. What is the value of | f(x) dæ? Writey your answer in simplest form. ...

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