Suppose a population of insects increases according to the law of exponential growth. There were 130 insects after the third day of the experiment and 380 insects after the seventh day, Approximately how many insects were in the original population?

Q: x dx is equivalent to If we let u = V 5+x, the integral 5+x A) u (5- B |u(u²-5) du (C | 2(u²- 5) du…

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Q: ſla(Ji + s)dt 1.

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Q: After evaluation, if tan 43rdr=-tan³3r– ( ? ) tan3r +r + C, then find the missing (?) term. 9. A 3 D…

A: In this question we have to find the Missing value in the Integral.

Q: x²-4 dx can only be evaluated using trigonometric substitution technique . The True B False

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Q: () If h(x) = | cosxdx and h =4, then h (0) is equal to 4 A -3 B 3 4 D -4 E) None C.

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Q: Let f(x,y) = C be the antiderivative of F(x) = x-cos(2x), Determine the value of C if x = 64 and y=…

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Q: dx The only solution to evaluate is using algebraic substitution technique. 3+V. (A True B) False

A: To find whether given integral can be solved only by algebraic substituion technique

Q: Question 13 sin2x cos3x dx = sinSxdx - sinxdx A) True B False

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Q: The standard form of 3dy-xydx= 3y%e*/3 by Bernoull's equation is: dx A Зе dy xy = 3e**/3,3 dx 3 x-…

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Q: x/4 The definite integral sin24x cos2x dx is equivalent to x/2 1 -sin20 cos20 de A x12 2sin20 cos40…

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Q: 1 csch2zdz=-In csch2z – coth2z +C 2 A True B) False

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Q: sin?u In tan"udu, where m is any positive integer, we use the transformation for tan?u= cos?u A True…

A: We have to choose the correct option according to the given information

Q: Find the equations of the tangent line and the normal line to the graph of the equation at the…

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Q: (x+1) dx If A B C + + dx ,the values of A & C respectively are (x+2) (x- 1)2 (x – 1)2 x+2 X- 1 3

A: We will evaluate the integral using partial fraction as following.

Q: dx is 2/x – Sin|/x +s|+c. Vx +5 The antiderivativeof | - A True B) False

A: To find the antiderivative of the function

Q: The x2-4 dx can only be evaluated using trigonometric substitution technique. A True False

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Q: Which of the following is one of the correct steps to evaluate cos3 dt to obtain the correct…

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Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

A: Given, x''+x=tant x=-costlnsec(t)+tan(t)x''=cos(t) ln(tan(t)+sec(t))+tan(t)

Q: aluate each of the following indefinite integrals: Show complete and detailed solutions. Express…

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 1, (1, 4) Vf(1, 4) =…

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Q: / [cosh²(2x²) – sinh?( 21²) ]dx is equal to A B dx c) None D x²dx E xdx

A: Let's find.

Q: Determine the value of C in on the antiderivative of F(x) = sin³(x)cosª(x) for x = 0.435 and y =…

A: Antiderivative of F(x)=cos4(x) sin3(x) isy=∫cos4(x) sin3(x) dx

Q: Question 6 To begin evaluating J sintrecor^rdx comvenienty, express: sin'x as (sin²x) ²and use the…

A: Here we put cos^5x as (cos^2x)^2 cos x and then  Use the identity cos^2x=1-sin^2x.

Q: Find the volume of the solid of revolution when the region bounded by the line y=x+2 and the curve…

A: The volume for solid of revolution between curves is the volume of object between a curve y=fx and a…

Q: Determine the value of C in on the antiderivative of F(x) = sin°(x)cos“(x) for x = 0.108 and y =…

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Q: Given that cos 0 terminates in quadrant I, then what is the 40 41 A and that angle 0 value of sin 0?

A: See the answer below

Q: Determine constants A and B such that the given piecewise function is continuous for all x. -1 if x…

A: Given query is to find the value of A and B.

Q: Which of the following will yield an inverse trigonometric function e2* dx A 4+e2r ydy B -16 wdw 25-…

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Q: Evaluate: Jycos2ydy 글sin2y-글vcos2y + 승sin2y+C A B 글sin2y+ 글ycos2y+sn2y+C © ranzy-ycoszy-anay + C D 글…

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Q: x² – 4 Evaluate:

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Q: Which of the following will yield an inverse trigonometric function?

A: answer is in next step

Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: sin4x, 1+ cos4x &- 2 (А) (B) cos?2x…

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Q: In Problems 11-15, verify that the indicated function is a solution of the given differential…

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Q: Use the areas shown in the figure to evaluate f(x) dx, y = f(x) Area = 1.5 5 Area = 0.8 a b d Area =…

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Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: sin22x = 1- cos?2x В cos²2x = 1-…

A: Check the identities

Q: Given sec A = and that angle A is in Quadrant I, find the exact value of sin A in simplest radical…

A: Topic = Trigonometry

Q: Determine if the following series is absolutely convergent, conditionally convergent, or divergent…

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Q: 9-4x2 In solving for the antiderivative of f(x) = using trigonometric substitution, is transformed…

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Q: Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use…

A: topic - Synthetic division

Q: (4x²+ 5x*)dx (x+1) (x²– 6x + 34) 2 By method of partial fraction, the integral can be evaluated when…

A: Please see the below picture for detailed solution.

Q: Evaluate:- 4 dx ④ -VR-4-2sec-1(즉)+c A =/x2 – 4 + sec + C (c) =2/x2 - 4 + sec -/R-4+2sec-1(즉)+c x2. +…

A: Integration

Q: Question 15 The x²-4 dx can only be evaluated using trigonometric substitution technique . A True В…

A: Follow next step

Q: 2.x +1 The antiderivative of f(x) = is (x – 3)² (x – 2) 2 7 +C 3 A F (x) = 5 ln 3 | 3 + 2 В F (x) =…

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Q: Evaluate: Je*cos(7e*)cos(4e*)dx.

A: We need to integrate∫excos7excos4exdxSubstitute ex=tDifferentiate x w.r.t texdx=dtThen∫cos7tcos4tdt

Q: Determine the value of C in on the antiderivative of F(x) = sin°X)cos"(x) for x = 0.579 and y = 1.3.…

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Q: xcos-1(x) If x =0.97 and y = 0.85, then value of C in the antiderivative of F(x) = is (use radian…

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Q: xi (9a“ –10) The antiderivative of f (x) = is F (x) = 30 where "a" is equal to

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Q: dx is using algebraic substitution technique . The only solution to evaluate 3+ A True В False

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Q: 119 Given sin A V 12 and that angle A is in Quadrant III, find the exact value of sec A in simplest…

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Q: 2m '+e-2m ) dm=2 12m dm (А) True B False

A: