1. Find the area of the region bounded above by y = eª, bounded below by y = x, and bounded on the sides x = 0 and x=1

Q: ameterize the plane through the point -3, -5, -1) with the normal vector (1, 4, 4) -t) = es and t…

A: We are asked to find the parametrize equation

Q: Evaluate f(x)) = the limit: 2x+1, 4x3, if a > 2 if i < 2

A: Given f( x ) = 2x + 1 ,  if x &gt; 2           = 4x - 3 ,  if x ≤ 2

Q: Given y = (5x + 3e*)6, find dy dx

A: Given: y=5x+3ex6 To find: dydx Required formulas:  Power rule: ddxxn=nxn-1 Chain rule: fgx'=f'gx·g'x

Q: #4) Determine the integration constant in the below indefinite integral using the accompanying…

A: q=∫(4t2+5t4+3t+2t)dt∫tndt=tn+1n+1+c

Q: Find a degree 3 polynomial having zeros -8, 4 and 7 and the coefficient of ³ equal 1. The polynomial…

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Q: 23. Use the given graph of f(x)=√x to find a number & such that |x4|< 8 if YA 2.4. 2 1.6 2 then 4…

A: By using the given graph of fx=x to find a number δ such that if x-4&lt;δ then x-2&lt;0.4.

Q: Consider the Cobb-Douglas Production function: P(L, K) = 22L0.9K0.1 Find the total units of…

A: given  P(L,K)=22L0.9K0.1given  L=15 K=13

Q: L' The Midpoint Rule approximation for -3x - 5x²) dx with n = = 3 is:

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Q: Find all zeros of the function f(x) = 6x³ - 17x² Enter the zeros separated by commas. 17x² 48x + 80.

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Q: Find the Laplace transform of the function √3, 0<t< 2π 0, 2π ≤ t < 00 f(t) = { NOTE: Express the…

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Q: Given that  lim x→3 f(x) = 1    lim x→3 g(x) = −4    lim x→3 h(x) = 0, find the limits, if they…

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Q: # 5) Evaluate the definite integral below (remember, like for all the other problems, show all your…

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Q: b) Rationalize the numerator of 1 1 √7(x+h) √Tx - h Simplify your answer to the form A = A " where

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Q: f(x, y) x² + y² - 1, (x, y) = (0,0). Applying the definition of continuity, explain if f(x,y) is…

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.)  lim          5-|x|/5+x x→−5

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Q: Given cost and price (demand) functions C(q) = 110q+47,300 and p(q) = -2.8q+880, what price should…

A: given  C(q)=110q+47300p(q)=-2.8q+880given  revenue is  $55000

Q: Determine the rational roots of 2x 5- 11x 4+ 14x 3- 2x 2+ 12x

A: Solution: 2x 5- 11x 4+ 14x 3- 2x 2+ 12x

Q: Find the equation of the plane containing all points equidistant from the points (3,-7, c) and (1,…

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Q: A company determines that its weekly online sales, S(t), in hundreds of dollars, t weeks after…

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Q: (1) Find the solution of the given initial value problem. t³y + 4t²y = e-t, y(−1) = 0

A: Let's solve given differential equation.

Q: Find two different planes whose intersection is the line x=3+t​, y=−2−t​, z=1−5t. Write equations…

A: Given: Intersection line equation: x = 3+t ..................... Eqn (1) y =-2-t…

Q: The following table records some values of the functions f and g. 0 1 2 3 4 5 21 36 X f(x) 10 3 10…

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Q: Tutorial Exercise Use partial fractions to find the indefinite integral. 16x1 dx Step 1 Rewrite the…

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Q: Let P(x) = (x - 1)(x - 2)² (x-3)³. Find the set of r such that x (a) P(x) = 0, (b) P(x) 0.

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Q: 1. The instantaneous velocity of an object moving along a horizontal line relative to a fixed point…

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Q: Find the indefinite integral. (Use C for the constant of integration.) [ (18 √x + √ / x) dx

A: We will use the following formulas of integration to solve this…

Q: Compositions of Functions In Exercises 41-44, find (a) fog, (b) gof, and, if possible, (c) (fog)(0).…

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Q: x < 1 f(x) = {-2x+2² ; x ≥1

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Q: Find the distance from the point to the plane (9,9,9)​, y+5z=0 The distance is _______________…

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Q: Consider the function f(x) = 3x^2 - 5x on the interval [-3, 3]. a) The slope of the secant line…

A: Given function f(x)=3x2-5x  on the interval [-3, 3]

Q: Evaluate the line integral 5xy² ds, where C is the right half of the circle x² + y² = 9.

A: Evaluate line integral

Q: Use the method for solving Bernoulli equations to solve the following differential equation. dy y +…

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Q: Three regions are defined in the figure. y C (0, 2) 0 R₂ /y = 2√√x about AB R3 y = 2x R₁1 B(1, 2) A…

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Q: 4. If f'(x) = 12x² + 6x −4, f(0) = 4 and f(1) = 1, find f(x) Ans f(x) = x² + x³ - 2x²-3x+4

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Q: Algebraic-Graphical-Numerical In Exercises 25-34, show that fand g are inverse functions (a)…

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Q: 1 -x²-10x+300, 0≤x≤60, where x is the 12 number of units of the product sold and p is the price, in…

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Q: 1. a. Write a set of ordered pair that defines the relation given in the graph. -0 b. Write the…

A: We see all values from given graph .

Q: Give an equation for the sphere with diameter PQ, where P = (1, 1, −3) and Q = (1, 9, 1). (Express…

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Q: f(x) = -5 ln(7x)

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Q: 2) If (2x + k)dx = 0, find k

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Q: Estimate the area between the x-axis and the graph of f(x) = 9 - x² over the interval [-2, 1] by…

A: Left end point approximation An = Area An = Ln = △x( f( x0 ) + f( x1 ) + ---- + f( xn-1 ) )

Q: A graphing calculator is recommended. Determine whether f is even, odd, or neither. Use technology…

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Q: Find the inverse for each relation. 1. {(1, -3), (2, 3), (5, 1), (6,4)} 2. { (-5,7), (-6, -8), (1,…

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Q: Suppose g(x) ≤ f(x) ≤ h(x)for all x near 1 (except possibly at 1). In order to use the Squeeze…

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Q: Find the derivative of ƒ(x) = x²e².5x ƒ'(x) =

A: Given: fx=x2e2.5x To find: f'x Required formulas:  Product rule: uv'=u'v+uv' Power rule: ddxxn=nxn-1…

Q: For the drug metabolism function f(x)=-x(x+2)(x-3), find the average rate of change of f(x) on the…

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Q: 1. Let a, ß E N. Let f(x, y) = x² + y² for (x, y) = (0,0). (a) Prove that the function f admits a…

A: Please see the below picture for detailed solution.

Q: Find an equation of the circle passing through the points  (−2, 3), (−5, 6), and (1, 2).

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Q: 1. Appoximate the area under the curve f(x) = x² − x + 1 over the interval [0, 3] using L6. Write…

A: We need to approximate the area under the given curve by using the left Riemann sum.

Q: Graph the function by hand, not by plotting points, but by starting with the graph of one of the…

A: The given function y=5+x+3. We have to sketch the graph of the function.