Find the slope of the curve ab²e-b²=5a-16 at the point (a,b) = (0,4) da ㅇ1 11 렇 O None of the above

Q: Part 1 Find the binomial coefficient. 7C5 20C15   Part 2 (Use the binomial theorem to expand…

A: Binomial Theorem: a+bn=C0nan+C1nan-1b+C2nan-2b2+C3nan-3b3+......+Cnnbn. Binomial coefficient:…

Q: (b) J₁ In x x3 dx

A: To determine whether the following integral is convergent  or divergent.  ∫1∞lnxx3 dx Note: Since,…

Q: Question 8 What are the domain, range, and period of the function f(θ) = –3cos(–2θ)? Answer in…

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Q: If A(t) denotes the annual rate of world consumption of oil at time t (with t=0 corresponding to…

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Q: Determine the following limit: 2e 2x Him (2²-2-2) x-0

A: limx→02ex-2x-25x2

Q: Find the area of the surface generated by revolving the curves about the x = sin t, y = 1 + cos t, 0…

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Q: 75 Compute the definite integral cos³ (2x) sin² (2x)dx . 4 30 2 15 1 15 6 775 10

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Q: 57) Given: f(x) = ax³ + bx² + cx+d, f(2)=5, ƒ"(1)=-4, ƒ"(4)=12 When x = 1 the tangent line to f(x)…

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Q: 3 What is f S₂² 1+1/2² dx ?

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Q: Find ve, where ||v|| = 11, e is a unit vector, and the angle between e and vis (Use symbolic…

A: v=11 ,e is unit vector and angle between e and v is 2π3

Q: ∞0 (x+1)" n=1 Vn4n

A: Use the Ratio test

Q: A normal vector to a line is perpendicular to that line. True O False

A: To find true or false statement: A normalvector to a line is perpendicular to that line

Q: 1a Differentiate the following functions with respect to t and simplify your answer as far as…

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Q: VIII. Find the equation of the plane with the given description. 1. Passing through P = (2,-1, 4), Q…

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Q: [200] Given E=1 42, determine, L3 3 1 1 the determinant of E. 2 the matrix of the minors. 3 the…

A: E=200142331

Q: Find the critical points in the domain of the function f(x) = 9x³ – 8x. Enter the exact answers in…

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Q: Evaluate the integral. (Use C for the constant of integration.) √ 8 tan³(x) sec(x) dx

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Q: given fal = √√x-5 and 9(x) = x² + 4x + 2 Find Fog and g of

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Q: Lines intersect in a point in two-space but do not intersect in three-space. True False

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Q: Show all steps to prove the statement is true. Neatly show each step of your work to earn full…

A: Given Trigonometric expression  ( 1 - sinx )( 1 + cscx ) = cscx - sinx

Q: Suppose f is a differentiable function of x and y, and the following applies. p(t) = f(g(t), h(t))…

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Q: 5. Which of the following is NOT an identit 1 - cos²x = sin²x 2 tan²x = 1 + sec¹x COSX sinx = cott…

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Q: What is the polar form of the equation? (x+6)² + y² = 36 O² 12r cos 0 Or(r+ 12 cos 0) = 0 ○r (r + 12…

A: x+62 + y2 = 36

Q: 8. A = (1, 1, -2), B = (-2,3,1), what's the angle between A and B?

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Q: find the general solution (GS) of the following initial value problem (IVP): y₁ = y₁ + 3y2 where y2…

A: The given system of differential equations: y1'=y1+3y2y2'=13y1+y2Initial conditions are:  y1(0)=12…

Q: Making this substitution using [₁ gives us 10 sin²(x) cos³(x) dx 10 10 sin²(x) (1 - sin²(x)) cos(x)…

A: To evaluate the following integral. ∫10 sin2x cos3x dx Note: After seeing the previous solution, we…

Q: Find the first few nonzero terms of the Maclaurin series for the given function. f(x) - In(1-3x)…

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Q: 1 cotx ln sinx|dx x In [ x Ja 2 1 2

A: To find, ∫ cotx2lnsinx2dx Let I=∫ cotx2lnsinx2dx We know that cot(x2) = cos(x2)sin(x2). Therefore…

Q: f f(0) = - = sin(1-0) Sketch the graph of f(0) = -

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Q: Sketch a graph of the function f(x) = 3sin x. Please state the range.

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Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

A: f(x)=-9x2.

Q: 9-12 Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer…

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: Solve ABC. Round the lengths of sides and measures of the angles to 1 decimal place if necessary. A…

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Q: If z = (x + y)e and x 2t and y = 1 — t², find the following derivative using the chain rule. Enter…

A: Function is  z=(x+y)ey, x=2t, y=1-t²

Q: Question 4 Given that sin() = 0.73, match each trigonometric function with its value. cos(8) csc (8)…

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Q: 2x cos(x²) esin(x²) dx

A: ∫2xcosx2esinx2dx

Q: Use the method of partial decomposition to perform the required integration. S 148 dz 2²46

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Q: Suppose 4²x = 12. Then x = A. In12 OB. (√12)³ 3 OC. 3 D. 109412 E. 09122 2

A: 1). logbxa=a·logbx  where x,b>0, b≠1 2). logbb=1

Q: A data-recording thermometer recorded the soil temperature in a field every 2 hours from noon to…

A: We need to find average temperature.

Q: 5. The graph below shows the function h(x) over the interval 7≤x≤7. At which x-values is h(x)…

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Q: Find a function f(x, y, z) such that V f = (8z, 4y³, 8x). (Use symbolic notation and fractions where…

A: Given that :-       ∇f=8z,4y3,8x  ⇒∇f=8zi^+4y3j^+8xk^  ....(1) Now we know that…

Q: Michelle invests in a savings account that pays 8% interest compounded monthly. What is the APY for…

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Q: Find the value of d2y/dx2 at the point defined by the given value of t. x-9 sin t. y - 9 cost, t =…

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Q: Find the indicated partial derivative. V = In(r4 + s5 + tº); Ꭷ3v ərəsət Ꭷ3v ərasət

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Q: Find the derivative of the function. f(x) = 2e³x-1

A: We have,      f(x)  = 2e8x-1

Q: Use the chain rule to find the indicated partial derivatives. u = xety, x = a²B, y = B²y, t = Y²a ди…

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Q: What is the rectangular form of the parametric equations? x (t) = t - 3, y(t) = 2t² — 1, where t is…

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Q: (a) Find a simplified form of the difference quotient and (b) complete the following table. f(x)=x²…

A: Given: f(x)=x2 We are required to: a. Find the simplified form of the difference quotient…

Q: Find the indefinite integral. Hint: u = x - 1 implies x = u +1. x(x-1)dx

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Q: a) Find the parametric equation of the line passing through the point (1, 5, -3) and parallel to the…

A: In this question, we can find parametric equation and value of k.