find the derivative of the following functions using the basic differentiation rules. use the proper notation. show complete solution.

Q: Why 3^(x+2)-10×3^(x)+1=0 is -2 or 0?

A: Put x=-2 or x=0 and check which 'x' satisfy the equation .

Q: 2n tan h 3x 3-) Arc sin tanh X

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Q: sets or parametric equations and symmetric equations of the line that passes through the given point…

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Q: 1 7. y = \x sin x,

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Q: Determine the value of C in on the antiderivative of F(x) = sin°(x)cos³(x) for x = 0.669 and y =…

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Q: sin x e" dx Cos x

A: To evaluate the given integral.

Q: Find the following using the table below. 12 3 4 f(z) | 2 3 1 4 f'(x) | 31 2 4 g(x) 3 4 2 1 g'(x) |…

A: Given data

Q: 4. The domain of the function f(x) = V3-1 is %3D and its range is. 5. The a-intercept of the line 5x…

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Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not…

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Q: If f(x, y) = (17x - y)3, then is given by: af dy (17x (17 – ) 13 - 18 (17x 13 - - 13 Y)2 – ) 18 (17x…

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Q: Select the correct graph of y = sinx, y = 0.2, and y = – 0.2. 03 Figure 1 Figure 2

A: We have to use properties of functions to solve the

Q: An jet travels horizontally at a speed of 500mph at an altitude of 3 miles above the ground. A…

A: We need to find the rate at which the angle of elevation is changing.

Q: representing all lines passing thru (-1,1)

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Q: Consider the following. u = (3, 7), v = (4, 6) (a) Find the projection of u onto v. (b) Find the…

A: We can answer both the question in the following steps.

Q: A body at a temperature 0 degrees Fahrenheit is placed in a room temperature is kept at 100 degrees…

A: Given query is to find the time required to reach the temp to 50° Fahrenheit.

Q: The integral of the given function f sin ucos udu is sin*u -sin*u +sin'u +C b. -sin*u +sin u+sin'u…

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Q: Determine whether u and v are orthogonal, parallel, or neither. u = -7i + 48j – k %3D v = 7i +j- k O…

A: Given u = -7i + 48j - k v = 7i + j - k

Q: Match the integral expression on the left to an equal expression on the right. Prompts Submitted…

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Q: Match the integral expression on the left to an equal expression on the right. Ssin(ax)sin(4x)dx +…

A: We know that; The trigonometric identitites; a). sinxsiny=12cosx-y-cosx+yb).…

Q: Solve

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Q: d100 y (100th derivatives) dx100 b.y = x100 ; find

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Q: Determine the value of the arbitrary constant of the antriderivative of F(x) = x-In(x) given the…

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Q: d) y = sinh(lnx)

A: As per your request I will solve d part

Q: Match the integral expression on the left to an equal expression on the right. Ssin(3x)sin(4x)dx -…

A: Let's find.

Q: dy dr * = 1+ ev-z+5 e + e®+y

A: Option -3:C=x e-5-ex-ydifferentiating w.r.t. x;0=x (0) + e-5(1) +exe-ydydx                -ex-y0…

Q: Determine the equation of the line that is tangent to y = elan"(2x) at x = 8

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Q: (За* + Зт?) da — ватат — 0 - a-'C = a² – m? 2 aC = a² – m? 2 Option 1 Option 2 С — а +т O Option 3 O…

A: Given problem:- (3a2+3m2) da  -6am dm=0 To find:- General solution of given differential equation

Q: Consider the following function and express the relationship between a small change in x and the…

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Q: Find the length of the following parametric curve. x = 6 + 916, y = 5 + 6t°, 0<t < 2.

A: solution is given below

Q: What is the equation of the vertical asymptote of f(x) = tan x where 0 < x < n

A: First draw the graph and get the vertical asymptot.

Q: // V9 - y? dA, where R= [0,4] × [0, 3] R V9 – y? is (Hint: In this question, since V9 – y? > 0 in R…

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Q: sin x e" dx Cos x

A: Given:       ∫sinxcosxex dx       =∫tanx exdx Integration by parts Formula:       ∫u dv=uv-∫v du

Q: (2x – y)dx + (4x + y – 6)dy = 0 -

A:

Q: The number of bacteria in a culture is increasing according to the law of exponential growth. The…

A: N(t) =N0 ekt  ...(1)N0 =260N(1)=260 ekN(8)=260 ek8N(8) =2 N(1)260 ek8 =2*260 eke8k =2 eke7k =27k =…

Q: [2x [8 5 Find the value of x+y, if 7 -y] 7 3 1. 4 2. 1 3. -3 4. 6

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Q: What is the equation of the vertical asymptote of f(x) = tan x where 0 < x < T А. х — 2 B. f(x) has…

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Q: From among the 36 students in a class, one president, one vice-president and secretary are to be…

A: It is given that, there are 36 students in a class. Out of which one is elected for president, one…

Q: 19. Which of the following illustrative equations will give a slope 10 of the tangent line to its…

A: A)y=2x2-2x at (2,3)Differentiate…

Q: Match the integral expression on the left to an equal expression on the right. Prompts Submitted…

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Q: Write the partial fraction form of the following expression: 4 x²+15x+56 Note: You are not asked to…

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Q: . Evaluate the limit of a function using the concept of Special Limits. et-1 t2-3t+5 + t2-1 1. lim t

A: Given that a limit problem and we solve this problem by using general property of limit.     Here i…

Q: xsin-(x) If x =0.03 and y = 0.62, then value of C in the antiderivative of F(x) = is V1-x2

A: Given  F(x) = x sin-1(x)1-x2

Q: Find the exact value of the expression. co(sn-() - cot-(V3)) 2 Need Help? Read It

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Q: [tan (x)sec (x)dx cot (x)csc°(x)dx sin (x)cos (x)dx

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Q: 2. If f(x, y) is a function of y only, then S" S fdxdy Si fdy. %3D

A: Given query is to find statement is true or false.

Q: - x cot 2y × CsC 2り Csc zy %3D dy

A: Integrating factor of the ODE of the form, dydx+y*f(x)=g(x) is given by, I.F= e∫f(x)dx ∫cot(mx)dx…

Q: The integral expression J xCos-(2X)dx can be evaluated using integration by Judv= uv- Jvdu Let…

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Q: Find the solution of the initial value problem y" + 2y' + 5y = 24e cos(2t), y(0) = 8, y'(0) = 0.…

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Q: (a) Find the dimensions of a box with a square base with volume 27 and the minimal surface area.…

A: This is an optimisation problem, we use derivatives to find critical points and use second…

Q: 5. In the given differential equation, eliminate the arbitrary constant. SHOW YOUR COMPLETE AND…

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