Find the slope of the tangent line to the curve 2x2 + 4xy- 2y = 142 - at the point (– 1, – 4).

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A: This question is based on finding equation of tangent line at a point on a given curve.

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A: We have to solve the value. 

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Q: (*+2x* -1) ? 5. What is f(-2) if lim, 5-3x 12 В. 6. C.- 15 D. -- А.

A: Given that: limx→-2x3+2x2-15-3x

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Q: Use synthetic division to divide (2x*- 3x³ - 5) + (x +2). State the quotient and the remainder.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first quest...

Q: Determine S5x? cos 2xdx

A: Given query is to evaluate the integral.

Q: Evaluate the following limits: z² + 4x – 12 3. lim 1² – 2x 191 S y² +5 _ify-2 4. lim g (y) where, g(...

A: 3. limx→2x2+4x-12x2-2x4.  limy→-2g(y), where g(y)=y2+5if y<-23-3yif y≥-25.  limx→4z-2z-4

Q: wer -0.7 Find -7 sec (5x + 4) tan(5x +4) dx. Show the steps th -1.1 S-

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Q: Provide a diagram where limx→a f(x) exists, f(a) is not defined and f(x) is not continuous at a. Wha...

A: A function f(x) has properties,limx→af(x) exits, f(a) is not definedfx is not continuous at x=a cont...

Q: 8. The rate at which ice is melting in a small fish pond is given by dv %3D dt V1 + 2, where V is th...

A: Let's find. 

Q: COSX (25) Find the area between the curve y= and x-axis and x 1/2, x 1/6 sin x

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Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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Q: Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the cur...

A: Using equation of tangent formula.

Q: 10. Bonus: Let y = Va + Vx + Vx+ ... to infinity. What is the expression for y'? (Hint: Try to find ...

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Q: Solve sin 40 cos³ 0 d0

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Q: Activity 1: For odd-numbered questions, determine the equation of the normal. For even-numbered ques...

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Q: Sx (x² – 2)14 dx

A: Use algebraic substitution to integrate then simplify. 

Q: 3.fCx)3D63X²4X+2 x<1 2x-1 X71 Part A: IS f(X) lontinuous ar X-1? JustfY answer. Palt B)EXPainunyfeX)...

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Q: 2 – 100 Evaluate the integral: (A) Which trig substitution is correct for this integral? Oz= 100 sec...

A: Given: ∫6x2-100x4dx

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Q: dx 3. Vx+3

A: Given query is to find the value of the integral.

Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the oute...

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Q: (a) Find the exact area of the surface obtained by rotating the curve y = e^x about the x-axis over ...

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Q: Use Table of values to detemine the limit

A: To use the table of values to determine the following limit.limx→0 5-x-x2  

Q: Consider two vector equations ℓ1 : ⟨x, y, z⟩ = ⟨3, 7, 4⟩ + t⟨2, 3, 1⟩, for some parameter t, ℓ2 : ⟨x...

A: Check the Ratio of direction ratios of both the lines. 

Q: Part A) What is im f(xh x-0 Part B) What is f(o) Part C) What is im f(x)> x-2 Pan D) What is im flxh...

A: a) limx→0f(x)=-1 b) f(0)=-1

Q: # 17 17. f(x)=- (2x+3) (x² +1)'

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Q: 1. S" cos? (2t) dt u-sub = 2. S sin5 0 cos* 0 d0 power on sin is 'odd'

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Q: Question Currently, the number of people entering a shopping mall is 109, It is estimated that the n...

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Q: -S; (4vw) dw

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Q: 2. Given r(t) = e' cos ti + e' sin tj+ e'k , find the tangential and normal components of accelerati...

A: Given: r(t)=et cost i +et sint j+et kTo find the tangential and normal components of acceleration:Fo...

Q: Use the matrices below to perform matrix multiplication. 5 10 4 C -10 0 12. 3 6 B -2 7 6. 8 If the o...

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Q: 4² – y² +25:² = 100 %3D

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Q: sin r lim ,3 81.

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Q: 20KdL do = 29000습 0.75in(+4) in 72 20dL d8 = o[29000]0.75 (36 + 4) 8=0.0134 inch ans

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Q: Find the DE of the family of plane curves described and sketch some of its member Circles tangent to...

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Q: 3. Sketch OP = (3, -4, -2) including the rectangular prism that frames it. Use and label the axes, i...

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Q: Consider the following function. Function Factors f(x) = 3x³ – x² – 9x + 3 (3x – 1), (x + v3) (a) Ve...

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Q: The base of a solid is the region in the first quadrant bounded by the curves below. 16x 16 – y? %3D...

A: We need to find the volume of the solid.Below find the solution in the image.

Q: 1. If ü= (2,-3), v=(1, -5), and w=(6, 2), determine the following: a) |ü +v| b) 3 ỹ -ū +w

A: a) u→+v→=(2,-3)+(1,-5)=2+1,-3-5=3,-8=32+(-8)2=9+64=73|u→+v→|=73

Q: Perform the calculation. 45° 17'- 29°48' 45° 17' - 29°48'= (Simplify your answers. Type an integer o...

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Q: Write your complete solution on the box provided after each number. Determine the standard form of t...

A: Solution of General equation of ellipse is written in step2 and 3

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Q: -1/2 -1/2 Step 2 Therefore, we have 3w - 7w + 5 - 3w3/2-7w!/2, sw1/2 Now, since the function is a su...

A: dwndw=n.wn-1

Q: Given that |ā| = 10, b| = 15 and d + b| = 17, then determine |3d – b|. Make sure to include %3D a fu...

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

Q: Find the value of the constant k that makes the function continuous. 2x-2x-12 if x+3 g(x) = , x-3 kx...

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Q: You are given the graph of a function f. Determine the Intervals where f is Increasing, constant, or...

A: Given graph of a function f