S- x² + seco tan de sece - 1 sec²0 de 1+tano sine de 1 + cose cose dᎾ 1 - sino The integral [se S I cost x dx x²_ can be transformed to which of the following using trigonometric substitution? 1

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: Compute the left and right Riemann sums L4 and R4, respectively for f(x) = √4x² on [-2, 2] and…

A: We can find Left and Right Riemann sums .

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

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Q: 2. Given: polar curves C₁ : r = √√√2- cos 0 and C₂ : r = √√√2 + sin intersecting at A(³√2, ³) and…

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Q: R(t) is a differentiable vector function for t > −1 with R' (t) = (1/1/² ,1 + t²) and R(0) =…

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Q: Find the inverse of 2=2-51.

A: Here, we need to find the inverse of z = 2-5i. So,…

Q: Find an equation of the line tangent to the graph of f(x) = (4x-7)(x+4) at (2,6). The equation of…

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Q: Find all critical points of the function y = e(3 e² (3 – x²). Then, using the second derivative…

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Q: The Intermediate Value Theorem can be used to prove that the equation 2²-2-15-0 has at least one…

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Q: Evaluate 3 TIT 4xyzdxydydz O 15 O 15/2 10 о None of the choices

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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: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

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Q: 26 Find the value of k so that line 4, 2]-[2-20]++ [2, k₁-3) is parallel to the Plane *x+24-42=12

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Q: lim f(z) = #t * NE

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Q: The cost (in dollars) of producing a units of a certain commodity is C(z) = 7000 + 18z +0.5x². (a)…

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Q: Evaluate the y' and Simplify the answers Inverse trigo functions y = √x² - 4+2arc(csc)

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Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: A company determines that its total cost, in thousands of rands, for producing x  items is (image…

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Q: 26. What is the value of lim A. - 2 B. - 1 1-cost t→0 t C.0 D. 1 - ?

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Q: 6. f(In x)² dx

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Q: dx 3-2x-x² L

A: According to our guidelines we can answer only one question. Other questions can be reposted.

Q: The polynomial function f is defined by f(x) = −2x² + 3x³ + 5x²-x-5. Use the ALEKS graphing…

A: We need to find local maximum.

Q: 1- Find the inverse of 2=2-51.

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Q: Exercises To Solve [No.5] dx 05². of зах (2) x²+2x+5 9x²6x+5 D

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Q: 4 The slope of the tangent line to the curve y = X at the point 5, is: 5

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Q: Ex: If f(3) = 0, show that əz дz x- x² + y = Z. (H.W.) əx Əy

A: We have to prove the given statement.

Q: Let C be the parametric curve defined by Ja(t)=1²-t-6, [y(t) = 41³ + 3t² - 6t. Determine the point/s…

A: a) Given that: xt=t2-t-6yt=4t3+3t2-6t For a horizontal tangent line, the slope must be 0. That…

Q: 6. Calculate the sum of the series: -396-308-220-132-... + 836

A: We have to find the sum

Q: Find the height of a circular cylinder of max. volume that can be cut from a spherical wood of…

A: using double derivative test to find out height when cylinder volume would be maximum.

Q: f(x)=8x¹-7x³+2 on [−2,1]

A: To compute the average value of the given function f(x)=8x4-7x3+2 on [-2, 1]

Q: A payment of $2,690 was due two years ago, and a payment of $1,650 is due today. What single payment…

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Q: line l: x = = and point P(1,0,1). ● Find the set of parametric equations of the line parallel to…

A: Both questions are solved.

Q: Tercises To Solve [No.5]

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Q: dx x√x-1 dx √8+6x-9x² 3. S 4. S

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Q: Solve the following differential equations: 2 √1-y² (a) - dx + y sin 2x -dy = 0 cos 4x+1

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Q: ƒ(x)=3x² +6x−9

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Q: 172. Evaluate the definite integral using the Fundamental Theorem of Calculus, Part 2. 3 La+…

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Q: Ex: If w cos(uv), u = = xyz, y = π 4(x²+y²)' aw find at point (1, 1, 1). əx

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

A: Here we have to use the concept of derivatives.

Q: Question Define Q as the region that is bounded by the graph of the function g(y) = 2√y+2, the…

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

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Q: 2- Compute 1+i 2-51

A: Given that,      1+i2-5i

Q: 6. If f is continuous and f² f(x) dx = 6, evaluate S/² f (2 sin 0) cos de.

A: see below the answer and calculation

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: Find Vector A and B such that A is parallel to , B is perpendicular to and A + B = if you already…

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Q: a. Find the first derivative. f'(x) = b. List any critical values. c. Identify intervals of…

A: As per the guidelines we can solve 3 parts only

Q: (b) Verify your answer in (a) using Stokes' theorem, where the normal vector to the surface has a…

A: We have to apply Stoke's theorem.

Q: -1 valuate the following expression without using calculator : tan sin (³²) +cos 35 - 12

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Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: 22. Calculate the arc length of the graph of (a) y = f(x) = 1⁄2x³ + x-¹ over [1,3]. Hint: (b) y = 1…

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