Verify that the function ƒ(x)=√x −x satisfies the three hypotheses Rolle's Theorem on the interval [0,9]. Find all numbers that satisfy the conclusion of Rolle's Theorem.

Q: Sketch the region enclosed by x + y² = 56 and x + y = 0. a) Favoring convenience, should you…

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Q: 0 5. 21 ) Let A=[¹²] and B= [¹ Find AB. 13

A: Given query is to find Matrix product.

Q: Evaluate the indefinite integral. √2³ √8 + zºda + C

A: The given integral is x5sqrt(8+x6).

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Q: Find the area of region enclosed by=t-t², y=t-t³, 0≤t≤1 using Green's Theorem.

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Q: Suppose that the radius of convergence of the power series    cn xn is R.      What is the radius…

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Q: (a) f(x)=2x+3x²-36x (b) f(x)=x+√l-x (1) Find the intervals on which f(x) is increasing or decreas…

A: first derivative 2nd derivative

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

A: Given: y=2x, y=5, 2y+2x=6 To find: Area between the above given curves Now, we need to find the…

Q: can you please explain in words how the equation 3y^2 + 2xy + x^2 = 6 turned into 6y+2y+2x+2x=0??

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Q: 1. Suppose that y is defined implicitly as a function of r by the following equation: 3y² + 2xy + x²…

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Q: Refer to the graph of y = f(a) with secant line PQ and tangent line PS. O PQ O PR O QR OQS OOO…

A: By the definition of dy  dy = f(x+ ∇ x) - f(x)

Q: Use the graph of f(x) to evaluate the following: 6 + 5 4 3 2 1 -1 f(x) 1 2 3 4 5 X Average rate of…

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Q: Given f(1) = 7, f'(1) = 5, if g(x) = ef(x) then g′(1) = (Give an exact answer)

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Q: Suppose F(4) = 6, F(6) = − 4, and F'(x) = f(x). 6 L² (2x²4 + 4 (x² + 4ƒ(x) + 10) dx

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Q: ) Inverse Laplace transform of 2S-5 2 + is s²+16 S3 f(t) = 2cos(4t)-5sin(4t)+t² F(s) =

A: NOTE: Refresh your page if you can't see any equations. . take inverse Laplace

Q: Evaluate the integral 24 2 (2³7) dz by making the substitution u = x5 - 7. > Next Question + C NOTE:…

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Q: If g(x) = f* √u² + 2 du, what is d²g / dx²? 0

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Q: If a loading ramp is placed next to a truck, at a height of 8 feet, and the inclined portion of the…

A: Given query is to find indicated angle.

Q: 4. Find an equation of the tangent plane to the surface z = xy+8 xy-2x at the point (1,1,–10)

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Q: For what values of h are the given vectors linearly dependent? 5 -20 -3 12 5 4 6 52 3 h Vectors are…

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Q: If f(8) = 2, write an ordered pair that must be on the graph of y f(x - 11) + 4.

A: Given data, f8=2 and y=x-11+4

Q: Solve the problem. [1 The columns of 13 = 0 0 O Suppose that T is a linear transformation from R³…

A: NOTE: Refresh your page if you can't see any equations. . here we have . so vector v1, v2, and v3…

Q: Let* (t) = (-5t² +4,t³-14, 21³). Find the line (L) tangent to (t) at the point (-1,0,2) L:(x, y, z)=…

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Q: What is dy given that y = ln (4- x? 1 x-4 dx 4 O I da I 4 dx 4-x

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Q: speed

A: We have to find the speed according to the given information

Q: Let f(t)= e¹t2 + cos(3 t) e5t then е L{f(t)} = ? O F(s) = F(s) = 2! (S-1) (s²+9) (s-5) F(s) = + 2! S…

A: Use property of Laplace

Q: The position of an object at time t is given by the parametric x=5t²+2t y=2t² +4 equations Find the…

A: Please see the below picture for detailed solution.

Q: A landscape architect in a botanical garden plans to enclose a 2000 square foot rectangular region…

A: Firstly we need draw and label the situation followed by construction of equation for the total cost…

Q: List each of the mistakes in the following calculations: d a) [(cos z)] = x(cos x)²-1 da d b) [(cos…

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Q: Given the ellipse below, determine the coordinates of the two foci. Enter the coordinates as ordered…

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Q: Match the following functions with the general shape of their graphs. Functions f(x) = ln (x + 2) -…

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Q: 13) Let f(x) = 4+4x x Compute f(x), f'(x), f'(x), f'''(x), f(iv) (x), f(v) (x) S f(), f'(), f), F"…

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Q: Solve for 8: cos²0 (1 + 2cose) = 0 on the interval 0 sesn. = 06-1플 100-10. ㅠ 3 품 품 3 3 00-27, 0.ㅠ…

A: To solve the trigonometric equation cos2θ1+2cosθ=0 ; 0≤θ≤π.   As the general solution of the…

Q: The rational function 310t V(t)= t + 2 models the velocity, V(t), in miles per hour, of a dragster t…

A: The rational function is given as  V(t)=310tt+2 The changed function of the velocity is…

Q: convergent serie 12) Find the sum of each 2 A) / + = + ( ² ) ² + ( ² ) ³ + ( ²1 ) 4 + ... ( - )^² +…

A: Let's find sum of given series.

Q: EXAMPLE 7 Sketch the conic below and find its foci. 25x²9y²-150x + 36y + 414 = 0 SOLUTION We…

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Q: Given the following equation of a circle in general form, find the equation in standard form by…

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Q: S Use Trigonometric Substitution to find the indefinite integral O 4v Y 4- y² y² 4(4- y²) + C O…

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Q: Find the matrix product AB, if it is defined. A = [56], B = [1 0-6 15 5 -18 12 OAB is undefined. °[…

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Q: Given f(x, y) Evaluate f(10, 8) f(10, 8) = 70x +90y - 5x² - 4y² - xy =

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Q: Simplify the trigonometric expression.   1 + tan(A) sec(A)  Step 1 Write tan(A) in terms of sine and…

A: Given query is to simplify the expression.

Q: Find the equation of the hyperbola with vertices (−3, 6) and (−3, −2) and foci (−3, 8) and (−3, −4).…

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Q: Which of the following is NOT true about the logarithmic function y = log a where a > 1? O It is…

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Q: Write the integral in rectangular coordinates, and then evaluate it. i) xyz dV where G lies below z…

A: Given that , z=1-x2 and the rectangle is R=x,y:-1≤x≤0 , 0≤y≤2 Evaluate ∫∫∫GxyzdV=?

Q: Consider the function below. f(x) = x²e-x (a) Find the exact value of the minimum of f for x ≥ 0.…

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Q: Use Integration by Parts to evaluate the definite integral 00 O O O -2 O -T 1- T TT x cos(x) dx.

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Q: If y = esin, then y" is equal to esin (cosa - sin x) A esindsinr O esinz (cos²x - sin x) O esin *…

A: Given that , y=esinx find y''=?

Q: ) If we would like to solve the following differential equation by variation of parameters 3x then…

A: We check whether the statement is correct or not .

Q: What is d dx 7x 3x O 102 sin z √2 - sint dt? O-3√2-Sin 3z - 7√2 – sin 77 O 3√2-sin 3x - 7V2 — sin 72…

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