Suppose that z + y = 82. dy (1) Use the method of implicit differentiation to find dr dy da (2) Find the equation of the tangent line at the point (z, y) = (1, – 3). The equation is y

Q: x1/2 dx reduces to Using an appropriate algebraic substitution, the integral 1+x32 2y2 dy 1+y3 ys dy…

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Q: 4. When the graphs of two functions intersect the angle of intersection is defined as the angle…

A: Slope of tangent

Q: A forest fire is found at midnight. It covers 1300 acres then. ... It is spreading at a rate of f(t)…

A: Given: A forest fire is found at midnight.It covers 1300 acres It is spreading at a rate of f(t) =…

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Q: Question 11 Evaluate: (ed"+1) /Ted" + 1)?-4 3x A) None B sec -C sec D sec-1 +C E +C 2 Sec-

A: First we put e3x+1=t and differentiate both sides with respect to t and solve it.

Q: To begin evaluating | sin*xcos xdx conveniently , express: A) None B sin*x as (sin?x)²and use the…

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Q: Question 10 Evaluate: Jevdx.

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Q: ,In sin –1x ) dx / sin(e n sin -x -cos(sin-!x) +C V 1– x² | A True B False

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Q: Which of the following trigonometric substitutions is the most appropriate to the intgral (4e2x +…

A: Given query is to find the most appropriate substitution.

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

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

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A: answer is in next step

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

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Q: Graph f(x) = e +2. Choose the correct graph. OA. Ay 4- OB. Ay OD. Ay Oc. Ay o 包

A: We need to choose correct graph.

Q: To evaluate sin 2x cos 2xdx conveniently, the formula/ identity to be used islare A sin²2x =1– cos2x…

A: We need to choose correct option.

Q: What is the general solution to the trigonometric equation? -V3 sec0 = 2 Drag the solutions to the…

A: Given, -3secθ=2 Divide by -3 on both sides, -3secθ-3=2-3 we have  secθ=-23

Q: 9=3 Sin 2X 2.

A: answer is in next step

Q: 3. lim f(x) = x³ - 1 %3D X 1 х-1 X approaches 1 from the left- -x approaches 1 from the right 1.001…

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Q: Given the following velocity function of an object moving along a line, find the position function…

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Q: Evaluate the line integral, where C is the given space curve.     Cxyeyz dy,   C: x = 4t,  y = 4t2,…

A: Firstly change the given line integral in terms of 't' and then solve.

Q: The result of the integral in 0 given 25 dy is 5 tane - 50 +C, y A True False

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Q: 1 6. cos-xdx cos* xdx xprt.

A: We need to solve the integral.

Q: Evaluate: ycos2ydy 1 1 A sin2y+ycos2y+sin2y+ C 1 1 B sin2y- ycos2y+ sin2y+ C 1 O'sin2y+ycos2y-sin2y+…

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Q: Find the critical points of the following function. 14x f(x) x2 + 49 Select the correct choice below…

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Q: On Melissa's 6th birthday, she gets a $4000 CD that earns 3% interest, compounded semiannually. If…

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Q: sin'x cos x dx (1– sinx)2(1+ sinx)? Evaluate: sin 8x

A: ∫sin7xcos5x1-sinx21+sinx2dx=∫sin7xcos5xcos2x1+sinx21+sinx2dx=∫sin7xcosxdxLet u=sinx.=∫…

Q: please

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Q: © J tane x*dx Using trigonometric substitution technique, the simplified integral after substitution…

A: sec2(x)-1= tan2(x)

Q: Determine whether the series converges, and if so find its sum. 1 %3D (k + 5)(k + 6) k=1 (Enter DNE…

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Q: Use the graph below to find the inflection point(s) and concavity:

A: Answer is in step 2

Q: 4. (entroid š pon! of intersetion of 3 mudiens of A hriangl. FAE Ba =/3 DE AG =43 AD (ent roid ond…

A: A triangle ABC, with median AD, BE & CF concurrent at centroid G. Also, AG = 23ADBG = 23BECG =…

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

A: Explained below

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

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Q: Question 14 If we let 4=V5+x, the integral -1 is equivalent to V5+x

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Q: The area of a circle increases at a rate of 6 cm /s. a. How fast is the radius changing when the…

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Q: Find the intercepts, critical numbers, intervals) of increasing and decreasing relative extrema,…

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Q: (x+1) dx B | dx , the values of A & C respectively are 9. -- (r+2)(x - 1)² = /+ (x– 1)², x- 1 3 (А)…

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Q: 3号x}

A: answer is in next step

Q: Find all the antiderivatives of the following function. Check your work by taking the derivative.…

A: We have to find the antiderivative of the given function.

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: Find the radius of convergence and interval of convergencE of the power series. (2х — 1)" 26. E 5"…

A: Use ratio test for checking the radius of convergence  and interval of convergence .

Q: V52 -9 dx 3x

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Q: dx Using half-angle substitution, the integral is equivalent to 2+ sin x dz A 1+z+z? dz B (1+z)² ©…

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Q: 3. .

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Q: dx The only solution to evaluate is using algebraic substitution technique. 3+V

A: Follow the procedure given below.

Q: Find an equation of the inverse relation. x=y² - - 7y Choose the correct equation below. O B. y=x -7…

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Q: a. f (x) sin x

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Use the compound interest formula to find the account balance A, where P is principal, r is interest…

A: Principal =$140000 Rate=4.5% Compounded =annually  Time=20.

Q: sin'x cosx dx Evaluate: (1- sinx)2(1+ sinx)2

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