QUESTION 3 Let f(x)=√x x and g(x)=x² Find gof(x) and state its domain.

Q: Let f(x) = The equation of the tangent line to the curve at the point (3,0.40000) can be written in…

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Q: What is the solution to the following DE?  d2y/dx2 + 5(dy/dx) + 6y = 0  A. y = A cos(-2x) + B…

A: The given differential equation is: d2ydx2+5dydx+6y=0   So, we can also write as; D2+5D+6y=0 The…

Q: Evaluate the integral of (3x²+9y²)dxdy if the interior limits has an upper limit of y and a lower…

A: Evaluate the integral of (3x²+9y²)dxdy if the interior limits has an upper limit of y and a lower…

Q: Find the fluid force on the vertical side of the tank, where the dimensions are given in feet.…

A: Fluid force=∫abρh(y)d(y)dywhere ρ is the density of liquid            h(y)  horizontal length of the…

Q: 3.) The revenue equation (in billions of dollars) for corn production in the United States is…

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Q: 1. Obtain the general solution of the given DE: (t² + 7st + 16s²)ds = −s²dt. The DE is homogenous…

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Q: Expression for the inverse of f(x) = e^(3x+1) f^-1(x) =?

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Q: √(√x − 2 csc xcotx + 1) dx is equal to 3 2x 2 3 3 2x 2 3 3 2235734 2x 3 3 2x 2 3 + 2 csc x + ln x +…

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Q: Suppose that f(4)=2, g(4)=5,f'(4)=6 and g'(4)=- 3 Find derivative h'(4) in (a) -(d) (a)…

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Q: Given f(x) = 2x² 3x + 4 - 2 g(x) = x² - 2x evaluate f(g(2)) + g(f(-2))

A: Given  f(x) = 2x2-3x+4  g(x)= x2-2x( Evaluate f(g(2)) +g(f(-2))

Q: Using the 4 step process to find f’ (x) f (x) = -3x^2 + 2x-7

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Q: If g(x) = 2 + x + ex, find g-¹(3).

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Q: Find the difference quotient f(z+h)-f(1) h for the function given below. f(2)=-7z+6

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Q: Cory puts a penny in her piggy bank on Monday, 2 pennies on Tuesday, 4 pennies on Wednesday, 8…

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Q: 10 Evaluate a(k - b)² in terms of a and b. k=0)

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Q: A toll bridge charges $1.00 for passenger cars and $2.25 for other vehicles. Suppose that during…

A: Topic- Linear equations we are given Toll bridge charge per passenger car=$1.00 Toll bridge charge…

Q: Find the average rate of change of the given function on the interval [4, 7]. h(z)= 3x² + 2x - 2…

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Q: Evaluate f f (x) dx if f(x) 06 O 12 8 O 14 = Į [2x X 1 if x ≤ 3 if x > 3

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Q: Find the fluid force on the vertical side of the tank, where the dimensions are given in feet.…

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Q: x²-4y+9=0

A: Given query is to find the domain and range of the function.

Q: Given the graph of y = J(2), shown as a red dashed curve, drag the green movable points to draw the…

A: given graph of y=f(x)  as a red dashed curve

Q: 16. dy dx = 4e-3x, y = 2 when x = 0 0

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Q: Given the vector function 7 (t) = (cos 2t, sin 2t, t), find 7(2), Ñ(1), B(4)

A: Given that  r→(t)=cos2t,sin2t,t

Q: 4-x 5-√√x² +9, lim x-4 5- 9-x² x-35-√√x² + 16, lim

A: To evaluate the limit.

Q: Suppose that f(x) = X 4x-8 Then, The domain of f is {x € Rx # Number} and ƒ-¹(x) =

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Q: use the function lnx. find the area of the region enclosed by x=1 and y=5 above y=lnx

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Q: 3. An aluminum rod 8m long has linear density √2+1 kg/m. Find the total mass and average density.

A: Total mass of a rod of length l of having linear density ρ(x) is ∫0lρ(x)dx.Average density…

Q: 1/271/20 Evaluate cos5 (0) de. Write your answer as a reduced fraction.

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Q: QUESTION 10 or 2-3e* +2=0, x=0 is a solution. State the other solution. Round/truncate to three…

A: Topic = Algebra

Q: 8. Find the position function r(t) given that a (t) = (-1,-1,-1) and 7(0) = (-5, -5,5) and 7(0) = 0.

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Verify if the primitive y = c₁sin (x) + C₂X defines the corresponding differential equation dy X +y…

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Q: Is the function, whose graph is drawn in Fig. 7. continuous at the following values of x? Figure 7…

A: To solve the problem of differentiability by seeing the graphs of the function.

Q: Let f(x) = x² + 9, g(x) = x − 8, and h(x) = √√x. Find the given compositions. Expand and simplify…

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Q: Calculate It t5/³ ln(4t) dt

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Q: Suppose that f and g are continuous functions such that f(1) = 9 and lim[ƒ(x) +6g(x)] = 13. Find x-1…

A: Topic- Limits and continuity if function is continuous at x=c at x=climx→c-f(x)=limx→c+f(x)=f(c) we…

Q: Evaluate composite functions Google Classroom Facebook Given: f(n)=-n² Step 2 (foh)(7) = f(h(7))…

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Q: 6. A company manufactures and sells x headphone per day. If the cost and revenue equations are:…

A: Cost Equation C(x) = 7000 - 2x   Revenue Equation R(x) = 10x - 0.001xSquare   Revenue if:-…

Q: lim (g4) co (y¹) (²2) y→0 24

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Q: Find the area of the region that is enclosed by the cardiod r = 10 — 10 sin 8. NOTE: Enter the exact…

A: Concept: The area of the region bounded by the cardioid is Area=∬Rrdθ

Q: Calculate (1/2 (2 (2t - 1)e³t dt.

A: Integrate ∫0122t-1e3tdt

Q: Evaluate the following expressions (note, you may not leave your answer as an algebraic expression)…

A: We use Logarithmic properties1. alogax=x2. lnmn=nlnm3. logaa=1

Q: Find the equation of the tangent line to the curve (a lemniscate) 2 (x² + y²)² = 25 (x² - y²) at the…

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Q: (1) (A × B) U (B × C) (2) AX (BUC) C = {9,10}, B = {7,8} , A = {4,5}

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Q: Given the curve r(t) = (cos 3t, sin 3t, 2t) Find the following unit vectors and simplify your final…

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Q: Find the derivative of the vector function r(t) = tax (b + tc), where a = (5,-1, 3), b = (-1,-5, 3),…

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Q: Given the functions: m(x) = √x + 3; n(x) = x³ − 4; p(x) = 9x − 5. Evaluate (m • (n − p))(3). A. 0 B.…

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Q: 5. Prove that x + y ≤ x − y + x + y for all x, y € R. Hint: Use the triangle inequality.

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Q: Let f(x)=(x+x^-1)^2. Find f'(5).

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Q: Suppose you deposit $1300 in an account with an annual interest rate of 5 % compounded quarterly.…

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