8. At what angle do the parabolas, y = ax and = 8 ay intersect? Ans. At (0, 0), 90°; at another point, tan-¹ crico

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A: To find all relative extrema of the function fx=4x4-32x3+3.

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Q: Suppose f(x) = { x² +1, x ≥ 3 2cx, x<3 Find a value of c so that f(x) is continuous at x = C.

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Q: Determine the derivative of = x³. f(x) = x³ when 2. f'(x) 3. f'(x) 4. f'(x) = 5. f'(x) 6. f'(x) =…

A: f(x)=x5xlnxn=nlnxd dx(lnx=1xd dx(a.b)=a×dbdx+b×dadx

Q: f(x,y) = e (3x² + 3y2)

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Q: 1. Consider the function f(x) = 412 - x² +8x| k +393 if x -5 (kx)² - 3 (a) Find the value(s) of k…

A: Given function is f(x)=412-|x2+8x|if x&lt;-5k+393if x=-5(kx)2-3if x&gt;-5

Q: Question 11 B The graph of a function fis is shown below. A Sketch the graph of the derivative f. Ⓒ…

A: Solving the following problem

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A: Inflection point

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Q: Find the derivative of the function using the definition of derivative. f(x) = x³ - 6x + 8 f'(x) = =

A: The given function is;  f(x)=x3-6x+8.

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Q: 1. Solve the following differential equations (D. dy 2 (a) du = (y − 1)¹/², y(1) = 1 dr 2x 4 dr 1 +…

A: As per the rules we are supposed to answer the first question and other can be reposted.

Q: Find by implicit differentiation. dy dx dy dx || 9 sin(x) + cos(y) = sin(x) cos(y) 9 cos(x) sin(y) +…

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Q: Prove: If a|b and b|c, then a|c. Hint: Use the definition of divisibility.

A: Prove: If a|b and b|c, then a|c.

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Q: Question 4 Classify each differential equation as separable, linear, homogeneous, bernoulli…

A: On solving this we will get

Q: . Let D be a region bounded by y = x² and x = y². Evaluate √ √(x² + 2xy + y²)dA

A: This is a problem related to double integration. Please follow the procedure given below.

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A: see below the answer and calculation

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Q: Assume A = A₁ + A₂ and A, B = 0. If A₂ = kB, show that k = ● (5) (6) Use the formula x = r' (t)…

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Q: 1 = (0) 1 = (1 + 1 = 0 - 1 - /

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A: Given g( x ) = x1 + x2

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Q: Q5. What is if y = 300(3x) +7sin(2x)- 8x37

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Q: Question #1 - Find the relative extrema for the function f(x)=2-3x-2x² using the first derivative…

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Q: 4. Utilize the method of substitution to evaluate each of the indefinite integrals below. 2x A. S…

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Q: Consider the function f defined by the formula 5x + 3(2x) f(x)=sin(ax) + ax² 4x² +8a-1 +5 if x > 1,…

A: Given f( x ) = 5x + 3( 2ax )         if x &gt; 1          = sin( ax ) + ax2      if x = 1…

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Q: For j(x)=(−2x2−2)(−3x2+2x), find j′(−1) by applying the product rule.

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Q: . Consider the function f: [1,4] → R defined by f(x) = x - √√x. A. What is the value of the signed…

A: Given: The given function is f:1, 4→ℝ defined by fx=x-x To find:  Find the value of the signed area…

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