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Q: For what value of the constant c is the function f continuous on (-∞, +∞)? cz +4 if x ≤ 10 f(x) =…

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Q: Given the following pieces of information: I. a = (4, -2, 3) II. b = (0, 3, -5) Find: a) lal b) ab…

A: According to our guidelines, we can answer only one question or three subparts of a question. Other…

Q: z = xey + y ex

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 2. Which of the following statements is TRUE? (Circle ALL that apply) a. |ū - v is always less than…

A: We need to check whether the given statements are true. We will check one by one.

Q: Determine the value of x when the slope is its maximum for the function f(x) = 2cos (3x)

A: Given,  f(x)=2 cos(3x)

Q: x-5 y+2_z+6 -2 5 d) is parallel to the y-axis, and passes through (6,-4,5) c) is parallel to *-=X+…

A: To find the vector equation of the line.

Q: 5. Calculate the sum of the first 23 terms of the sequence defined below. tn 10+ 3n, n E N

A: We have to find the sum

Q: What is the value of f(1) - 16B in [x³ Inx dx = f(x) ((1/4) Inx - B) + C? (A) 1 B) 2 C) 0 D 3

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Q: Let line l : x=y/2=z/3 and point P(1,0,1). Find an equation of the plane (in point-normal form)…

A: Solution of given question is written in below steps.

Q: The height s (feet) of a ball hit into the air is given by s(t) = -16f² +50t + 5, where t is the…

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Q: 23. Consider the circle x² + y² = R². (a) Write down parametric equations to traverse the circle…

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Q: Determine the equation of one of the curves for dy/dx = 4x which passes through the point (2, 3).…

A: We need to find a curve for dydx=4x which passes through 2,3.

Q: 36. Let d; denote the hours of daylight and 8; denote the increase in the hours of daylight from day…

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Q: eading due north at 500 km/h. If it encounters a wind from the northeast at 1 sultant velocity…

A: We will solve the problem.

Q: Exercises To Solve [No.5] OS s dx (x-1) √x²2x-3 3-2x-x²

A: Explained below

Q: The limit below represents the derivative of some function f(x) at some number a. 4(3 + h)³- - 108…

A: This question can be solved by applying the concept of first principle.

Q: Two vehicles start out traveling side by side along a straight road. Their position functions, shown…

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Q: If f(x) = 10, find f'(-1).

A: Given f(x)=10,  to find f'(-1) Formula used Differentiation of a constant value is zero d (constant)…

Q: 10 Determine the area above f(x)=x²+2x+3 and below the line y=11.

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Q: Find the slope of the tangent line to the graphof the polar equation 1 r = at Ø= 1-sinø 6

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Q: Given the vector function r(t) = (+1, 1-2t², 8t-4), find the are length of this curve on the…

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Q: Find the volume of the solid generated when the region ? bounded by the given curves is revolved…

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Q: 5. Suppose f is continuous on [2, 8]. Use the table of values of f to f(x) dx using a left, right,…

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Q: (C) Find dx (i) y= for the following functions : 3x 2x-1 2x+1 (ii) y=sec(sec ¹5x)+e5lmx +4

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Q: Find the derivative of f (w) = 7ln (w) + 18.

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Q: Exercises To Solve [No.5] Lim 9-5 a -4 dx ·8X-15 6 Sinx+25inx+5

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Q: Use the slopes of tangents to determine whether the function -6x2+36x is increasing, decreasing, is…

A: Given function, f(x)=-6x2+36x We know that function is said to be increasing when f'(x)>0, and…

Q: Use the limit definition of the derivative to find the instantaneous rate of change o ƒ(x) = 5x² +…

A: We have to find rate of change

Q: 2π 3 [³* sin(y) + sec² (y) dy

A: We have to evaluate the given integral.

Q: Question 2. Find the limit, if it exists, or show that the limit does not exist. (a) 4xy (2,3)—(0,0)…

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Q: x-4 x²+2x-15 Inx+51-Inx-31+ C 8 Option 1 S: dx 1 (x + 5)⁹1 Je In + C + x-3 -100 1 9 In|x + 5|ln|x −…

A: We can find the answer as below

Q: WAN 1 2 3 4 The graphs of 4 functions are shown above, and the graphs of the derivatives of those…

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Q: Find a set of parametric equations for the curve of intersection of the paraboloid z² +4y² -z = 0…

A: Here, to find the parametric equation of the paraboloid x2+4y2-z=0 and the plane 2x-z=0

Q: Find the particular solution of dy/dx=6e^3x+1,andf(0)=0.

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Q: I co cos³ x sin x dx

A: Given problem:- ∫cos3(x) sin(x) dx

Q: 37. Evaluate: A. In x + C B. 3. ——2+C x² dx. C. In x D. ). - 17/7/²2

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4. Express the following limit of the Riemann sum n lim (x + x² cos x; ) Ax, n→∞ i=1 ㅠ where x₁ =…

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Q: In x Compute -dx. 3√√/x 9 X 3 A²x²0 nx-x²²+ C A.- In 2/3 2 4 1 B.- - +C X 3 4/3 4 3 C.--(In x)x-4/3…

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Q: 2. Evaluate 3 dx -) S (x+5)(2-3)dx, (b), (c)²-22²-da, J ■) x³ −2x² −4 −1+ int: (c) 1 + ² + ²/1/2 x³…

A: Topic:- application of integration

Q: Differentiate the function: y = e-x cos²x x²+x+1

A: To differentiate the function.

Q: T. (3x² - 4x¹ + 2)dx -1 -3

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Q: if a 3 letter word is formed by randomly choosing 3 letters from the word PAINTED, what is the…

A: This question can be solved using the concepts of permutation and combination.

Q: Given: 3zxy Find fx O xy/3 O y/3 O x/3 None of the choices

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Q: Let S be the surface with equation (z - 4)² = 4x² + 4y². Viewing S as a surface of revolution, find…

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Q: Prove Formulas (1) - (9) Differentiate y = √3x². - 1 √5x = = (3x²)¹/³ – (5x)−¹/2

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Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

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Q: 18

A: We will solve the problem

Q: 6. f(In x)² dx

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Q: Q4: Convert the following polar integral to Cartesian Integral in order (1) dx dy (2) dy dx T 6 csc0…

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Q: 2. a+b+c=c+b+a is true because of

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