[1+2p(x-1)+(x-1)² x≤1 x>1 [qx+p -) -) Find the values of q, in terms of p, for which fis continuous at x = Find the values of p and q for which fis differentiable at x = 1 If p and q have the values determined in part b, is f" a continuous Justify your answer.

Q: Then calculate (b) lim xªsin()

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Q: Then find the length of the indicated portion of the curve r(t) = 5costi + 5sint j +9t k, where

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Q: State the derivative. Do not simplify. f(x) = - x² +3 X

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Q: Find the indicated partial derivative. f(x, y) = sin(5x + 4y); f yxy fyxy(x, y) =

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Q: Find T, N, and B for the curve r(t) = (0,5t, 51²) at (0, 25, 125). Hint: After finding T, plug in…

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Q: Find the indicated partial derivative. V = In(r³ + s + t5); a³v ərasət || 4 a³v ərasət

A: A detailed solution is given below.

Q: 2. Use the graph of f(x)=x² +3 to find a number & such that |f(x)-5.25|< 0.1 whenever |x-1.5|<8.…

A: Given that the graph of function f(x)=x2+3We have to find δ such that |f(x)-5.25|&lt;ε, whenever…

Q: Let f(x) 3x2+6. Evaluate lim h→0 f(4+h)-f(4) h

A: Solution ⇒     f(x)=3x2+6    and we have to perform  limh→0f(4+h)−f(4)h    Now put…

Q: Let h(x)=x^2+x+2 Let g(x)=^2√x−1 Find the following: (a) g(h(x))=   (b) h(g(x))=   (c) h(h(x))=…

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Q: Determine the center and radius of the circle. Write your answers as simplified fractions or…

A: The answer is in step 2.

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Q: Find the angle between the vectors a = ⟨1,0,1⟩ and b = ⟨1,−1,0⟩

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Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. an n! 53n…

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Q: Consider the following. Find the following partial derivatives. az as az at дz ди Find az Əs дz at…

A: Consider the following. z=x4+x2y, x=s+2t-u, y=stu2To find the partial derivatievs ∂z∂s, ∂z∂t,…

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Q: The following chart shows "living wage" jobs in Rochester per 1000 working age adults over a 5 year…

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Q: An arc of length 19 meters subtends a central angle of 288 in a circle. a) Find the circumference of…

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Q: IrT: R² R² is a linear transformation such that then the standard matrix of T is A= ¹([:])-[23] and…

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Q: At the beginning of the year 1995, the population of Townsville was 3819. By the beginning of the…

A: Let t = 0 , population ( P ) = 3819 t = 19 , population ( P ) = 4740

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A: Given plane equation:- -2y+4z=4

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Q: 3. Sketch a graph of y = 2 sin(2x - π) + 3. √√√ List below 5 points of 1 cycle.

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Q: 2 -[-3] Span (u, v) for all h and k. 21. Let u = and v= [2]. Show that is in

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Q: 1. For positive numbers a ≤ b, the pulse function is defined as ← a. Sketch the graph of the pulse…

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Q: Let f(x) = x²_ - 16 X-4 . (a) Calculate f(x) for each value of x in the following table. (b) Make a…

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Q: Suppose f(x)=√x + 2. Evaluate the limit below by using algebra to simplify the difference quotient…

A: NOTE: Refresh your page if you can't see any equations. . here we have x=8 . substitute x=8+h

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A: Topic:- application of calculus

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Q: Find the distance from the point (-5, 4, 5) to the plane 4x-3y-4z=-1

A: To find the distance from the point -5, 4, 5 to the plane 4x-3y-4z=-1.

Q: A solid is obtained by rotating the shaded region about the specified line. about the y-axis V = 5 0…

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Q: Use the graph of g in the figure to find the following values, if they exist. a. g(0) b. lim g(x)…

A: NOTE: Refresh your page if you can't see any equations. . as we can see from the graph, point (0,4)…

Q: P(1, 0, 1), Q(-2, 1, 3), R(6, 2, 5) (a) Find a nonzero vector orthogonal to the plane through the…

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Q: f(x) = log(x) + log₂ (x)

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Q: 8. If f(x) = √2x + 3 and g(x) = x - 1, what is the domain of g(x)f(x)?.✓✓

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