Find the following indefinite integrals subject to the initial conditions a) y'= with y(1)=0 x²+6'

Q: se the chain rule to find the derivative of f(x)=4√2x3+7x8 Type your answer without fractional or...

A: given f(x)=4√2x3+7x8 f'(x) = dfdx        =d42x3+7x8dxwktda+bdx = dadx+dbdx

Q: 3. Given the graph of y =f (x)below, on the same set of axes draw a graph of y =f (x). the concept (...

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Q: 22+22

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Q: () = 2 sec(a O conon1 O pton 2

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Q: A ball is thrown downward with a speed of 15 ft/s from the top of a 225-foot-tall building. After t ...

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Q: X = 6. (x)f (q (x 3. = (x)6 (3x 1. Determine the first derivative of the following functions:

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Q: 2. Consider the shaded region to the left of the y-axis bounded by the curves y = x2 – 1 and y = x2/...

A: 2) Here, the region is bounded above by the curve y=x22 and below by y=x2-1.

Q: For the function f graphed in the accompanying figure, find the following limits. If a limit does no...

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Q: Using Variation of parameters, find ui for the DE: y" – 2y' – 8y = 18e4* when Yc = Ce-2x + C2e4*. А....

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Q: Let C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are ...

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Q: Evaluate the slope of the function: (Please solve using limits)  f(x) = 1 - x^3                    ...

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Q: Current Attempt in Progress 1, determine whether the sequence converges, and if so find its limit. F...

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Q: An insect is tracing an elliptical boundary of a hot plate. The ellipse equation is given by+ = 1. I...

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Q: In cos (x - c1) + c2 y = In cos x +cj + c2

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Q: A ball is thrown downward with a speed of 19 ft/s from the top of a 361-foot-tall building. After t ...

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Q: If s(t) = 4t3 – 6t – 24t + 6, represent the position of a particle %3D traveling along a horizontal ...

A: Solution is here

Q: If s(t) = 4t°- 6t-24t +8, represent the position of a particle traveling along a horizontal line. De...

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Q: Calculate the derivative. y = cos 3x In (cos ²3x) y' =D %3D

A: We can find the derivative as below.

Q: ((2x-y²)´ (x,y) # (0,0) Let f(x, y) = x2+y4 2, (x, y) = (0,0) Is f continuous at (0,0)? Do fr(0,0) a...

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Q: Given: cosg= sin x = - 12, A is in the third quadrant, and x is in the fourth quadrant; evaluate tan...

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Q: Find f'(x) and find the values(s) of x where f'(x) = 0. f(x) = (2x – 21) (x² + 18) f'(x) =O

A: We will find the derivation of functions as follows 

Q: 12. Let F(x, y) = esinx+cosy(cos x ,– sin y) and C = {(x, y): x² + y² 0. Show that F- dR = 0 Hint: ...

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Q: Find an equation for the line tangent to the graph of  F(x)=6xe^x at the point (a,f(a)) for a =3 ...

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Q: Find the derivatives of the functions in Exercises 19–40. 24. r = 6(sec 0 - tan 0)³/2 26. y = sinx –...

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Q: Let f be function such that F(1)=6  and F'(1)=-11 Find h′(1) for the function h(x)=f(x)f(x) h'(1)...

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Q: Consider the following. dt 49 + t2 Let t = 7 tan(0) and determine the following. %3D dt d0 t = 0 → 0...

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Q: Given (x³ + y² + 7)* = 4x + 3y + 9, (a) find y', (b) find the equation of the tangent line at (-2,0)...

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Q: ASAP PLZ Find the moment of inertia with respect to x-axis of the region in the first quadrant, whi...

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Q: Determine whether each of the following functions is (a) continous (b) differentiable. Show a comple...

A: Determine whether the function is a) continuous.b) differential.show a complete solution. 1.f(x)= x^...

Q: 3 5 Given: cosa = ? and A is located in the fourth quadrant; find tan . %3D tan DIN

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Q: 6. [Geogebra Question] The altitude (in metres) obtained by an object t seconds into flight is given...

A: To find the maximum height of the object.

Q: Find the linearization L(x) of f(x) at x=a. f(x)=x/2x+9 a=0

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Q: How

A: We will find the solution. 

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

A: Telescoping series is the series in which all but the first and last terms cancel out .

Q: sine sece = O cote O tane 01

A: Given sinθ*secθWe know that secθ=1cosθ

Q: An artificial wetland has been created by building an earth dam across a small creek, between the si...

A: I am attaching image so that you understand each and every step.

Q: Consider the following sequence: +00 9" {a,} = An+1 - to show that the given sequence {a,} is strict...

A: The given sequence is  an=9n4n2n=1+∞

Q: Given: cosg= -, sin x= - 13, e is in the third quadrant, and x is in the fourth quadrant; evaluate t...

A: Given,            cosθ=-45 , sinx=-1213 , θ is in the third quadrant and x is in the             fou...

Q: A ball is thrown downward with a speed of 12 ft/s from the top of a 144-foot-tall building. After t ...

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Q: If r = c is a critical number of f, then f has a local extrema at I = c. True False

A: This question can be solved by applying the concepts of relation between critical points and local e...

Q: 13 5 Given: cosa = and A is located in the fourth quadrant; find tang. -5/3 -4/3 -5/4

A: Given that cosθ=35θ lies in 4th quadrantfind tanθ

Q: Find the derivative using the formula f'(x)= g'h + gh' 1. cos x cot x Let g= cos x, and h= tan x. ...

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Q: 3 If z= then: (2x² + y² )² ' dz az + y- -4z he dz dz + y- 4% az dz + x- y- = 4z az az = -4z

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Q: If x = c is a critical number of f, then f has a local extrema at I = c. True False

A: Question: If x=c is a critical number of f then f has a local extrema at x=c 

Q: Select the best answer. sin x 1+ cosx + sin x 1+ cosx

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Q: · 8x² + 8x + 2 =dx (4x² + 1)

A: 4X^2+1 cannot be fractionised further

Q: If s(t) = 4t3 – 6ť² – 24t + 8, represent the position of a particle traveling along a horizontal lin...

A: Let's find. 

Q: The position of a hummingbird flying along a straight line in t seconds is given by s(t) = 2t-9t met...

A: s(t)=2t³-9t meter  (a) Velocity=v(t)= d/dt(s(t)) v(t)=d/dt(2t³-9t) v(t)=6t²-9 Velocity at t=5 second...

Q: The position of the particle at time t is given by s(t) = t? 10t + 24. The particle is moving from r...

A: solution is given below..

Q: 3. Find the derivative of the following functions using the increment method. (10 pts each) 6- 3x 1 ...

A: a f(x) = 1/2-x now using increment method f'(x) = limh→0 [f(x+h) - f(x)]/h f'(x) =limh→0 [1/ 2-(x+h)...