True or false: If f is a function such that lim f(x) = L and x→a+ lim f(x) = L x-a where a and I are real numbers, then f is necessarily continuous at x =a.

Q: d the derivative of :) = €5* (x² +9¹)

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Q: Given that f(x) = x³h(x) h(-1)=2 h'(-1)=5 Calculate f'(-1). -20 Hint: Use the product rule and the…

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Q: Let f(x) = (6-x-x² 2x - 9 Calculate the following limits. Enter "DNE" if the limit does not exist.…

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Q: The limit represents f '(c) for a function f(x) and a number c. Find f(x) and c. [9 3(1 + Ax)] - 6…

A: limΔx→0[9−3(1+Δx)]−6Δx

Q: For the given parametric equations, find the points (x, y) corresponding to the parameter values t =…

A: Given,

Q: Add the following complex numbers. (−5+19i)+(3−3i) Give your answer in complex standard form a+bi

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Q: Use the graph of the function f shown to the right to estimate the indicated function values and…

A: To find:-The given graph

Q: Evaluate the indefinite integral. +C 5- 4 sin x Cos x dx

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Q: Evaluate the indefinite integral S 16 (49 - x2) 19/2 dx

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Q: f(x) = 3x5 — 25x³ + 60x on [−2, 3]

A: f(x)=3x5−25x3+60x on [−2,3]

Q: 4. Se 1+e 2x 5. fe²x sin 3xdx

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Q: Which step is part of finding the derivative of the function below? The correct choice may not be in…

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Q: Let f(v) = V v+17 v + 12 Determine the critical values of f. Write exact answers. Do not round off.…

A: A point x=c is  a critical point of the function f(x) if f(c) exists and if  f'(c) =0 or f'(c)…

Q: Determine the interval(s) for which the function shown below is decreasing. -8-7-6-5-4-3-2 8 7. 6 y…

A: given graph of the function

Q: SYSTEM: x + y + z = 6 2x - y + z = 3 3x z = 0 -

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Q: Verify the following identities: 1. tan y csc y 2. 3. tan x sec x = sec y cos y sin x cot x sec x…

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Q: Solve for x. 3x = 22 Select the correct choice below and, if necessary, fill in the answer box to…

A: The given equation is

Q: a. Find all the intersection points of the following curves. b. Find the area of the entire region…

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Q: Differentiate. g(x) = log 29 (5x-4) g'(x) =

A: To differentiate the following function.

Q: Given C = x³ – 6x² + 9x +4 13 a) Find C'(x) = Find any critical values of C'(x) b)x= Use interval…

A: Given,

Q: 0 1 3 2 X f(x) f'(x) -2 -1 2 N 2 133 When x = 0 then D 1 255 324 X 0 3 g(x) 1 2 g'(x) 2 3 -2 0 g(x)…

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Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A: In this question, we will draw the graph of the parametric equation.

Q: Write out the form of the partial fraction decomposition of the function appearing in the integral:…

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Q: 2. We found a solution y-sinx for the following differential equation. y"+y=0 a. Use Reduction of…

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Q: Find the exact directional derivative of the function √y z at the point (1,9, 9) in the direction…

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Q: Find the particular solution of the differential equation x²y" - 5ay +9y=9x (x > 0) satisfying the…

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Q: What are the critical points of f(x, y) = x² – 3xy — 1? (0,0) (1,1) (0,0) and (1,1) (1,-1) (1,1) and…

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Q: Use the properties of inequalities to solve the inequality. Write the solution set using set-builder…

A: The inequality is given byTo determine: The solution of the inequality.

Q: Use the quotient rule to find the derivative. x² + 8x +3 y= √x OA. dy 2x+8 dx X B. O C. dy dx dy dx…

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Q: v+1 v-15 Determine the intervals on which g is concave down. Consider g(v): Og is concave down on: O…

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Q: Find the following using the table below. X 1 23 4 f(x) 4 32 2 1 ƒ'(x) || 2 1 4 3 g(x) 34 1 2 g'(x)…

A: we are given the table of functions and their derivative at certain values, we need to find out the…

Q: Use a graphing calculator or computer to verify the given linear approximation at a = 0. Then…

A: The given function is

Q: A company is planning to manufacture snowboards. The fixed costs are $100 per day and total costs…

A: Given that,The company manufactures snowboards. The fixed cost is $100 per day and total cost $5100…

Q: Find a formula for the nth partial sum of the telescoping series below and use it to determine if…

A: ∑n=1∞(n+6−n+5)

Q: Let F = (z, xy, x² + y²). Compute the work done by the force when moving a particle located at the…

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Q: Find the volume of the region under the surface z = xy² and above the area bounded by x = y² and x +…

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Q: Find the logarithm using the change of base formula. log 590 log 590 = (Round to four decimal places…

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Q: -6 -5 -4 -3 -2 -1 6 5 4 3 2 1 0 -1 -2 3 A G -6 1 2 3 4 5 6

A: From the given graph

Q: Solve the absolute value equation for x. (Enter your answers as a comma-separated list. If there is…

A: To solve the following absolute value equation for .

Q: Solve the differential equation. (t−8) s' +7(t−8)5s=t+8, t> 8

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Q: Find I, I, I, X, and y for the lamina bounded by the graphs of the equations. y = √√√x, y = 0, x =…

A: The region is bounded  by The graph of region

Q: For each of the indefinite integrals below, choose which of the following substitutions would be…

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Q: Differentiate. f(x)= x³ In 7x 3 f'(x) =

A: Product Formula for differentiation is given as follows

Q: For the function x f(x) = x-5 find the derivative of the inverse function f-¹ at the point x = 2.…

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Q: dy dx - 5ln(t), y = 4t² - 4t-2

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Q: At what point on the curve x² - y² + x² = 0 is the tangent line vertical? (a) (0,0) only (b) (-1,0)…

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Q: Consider a trapezoid that has a constant area of 300 cm. The height of the trapezoid is increasing…

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Q: Find the value by writing the argument using the number 5 and using the value log 5 = 0.6930. log 25…

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Q: Write an equation for the function graphed below. The y intercept is at (0,0.2) N ? 7 6 a

A: The given graph

Q: 1. Isolate X.8 (3 + x-4) 4 24+ T (3x + 1 8 = 3x + 1 2x-8 24-9 = X X = 15 T 8

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