Using all three conditions of continuity, determine if the following functions are continuous at x = a. 3. h(x) = 1-x² 1 X x < 1 , x≥1 Write your conclusion in sentence form.

Q: Find the given limit. lim x-5 lim X--5 (-x²+3x-7) (-x² + 3x-7)= (Simplify your answer.)

A: Topic = Limits

Q: Find the perimeter of the triangle whose vertices are (-1,-2), (11,14), and (-1,9). Write the exact…

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Q: A company wants to increase the 20% peroxide content of its product by adding pure peroxide (100%…

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Q: [2-2 2 Let A 7 -4 10,6: 4 -4 4. Select true or false for each statement. Warning: you only have 2…

A: Given that A=2-227-4104-44, b=-2-11, and c=-2-4-4. We have to find the vector c is in the image of A…

Q: (e) lim (3x²-x¹ + 1) 818

A: Given Limit,e. limx→∞3x2 - x4 +1

Q: f(x) - √x² - 4, x ≤ 0 1 - 2x², x > 0 (b) f(0) (a) f(-2) (c) f(1)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Using partial derivatives, which one is equivalent to dz/dt, given z = x² + 3xy + 5y2; x = sin t, y…

A: Given that z=x2+3xy+5y2, x=sin t, y=cos t. We have to find the value of dzdt.

Q: It takes 1400 J of work to stretch a spring from its natural length of 1 m to a length of 3 m. Find…

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Q: Your family likes to eat fruit, but because of budget constraints, you spend only $5 each week on…

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Q: 5. Solve (y² + 3xy³) dx + (1 - xy)dy = 0.

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Q: In a sales promotion, a clothing store gives its customers a chance to draw a ticket from a box that…

A: In a sales promotion, a clothing store gives its customers a chance to draw a ticket from a box that…

Q: 0.015t The population of a town is increasing at a rate given by P'(t) = 47e where P is the…

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Q: Question 19 Find y' if y = 3acos x - 3 cos-¹x1n3 COS y'= y'= y'= y'= 3 cosx1n3 /1-x² 3 cosx1n3 - 3…

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Q: Assume that the function G(x) is measured in blips and x is measured in fonks. What units would…

A: Given :Assume that the function G(x) is measured in blips and x is measured in fonks

Q: Let a = (-5,3, 2) and 6 = (2, 1, -3). Find the angle between the vector (in radians)

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Q: Write an equation for the polynomial graphed below + -5 -4 -3 -2 Z 6 + 5 + 4- 3 2 7 بنا -4 ++ ++ -5.…

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Q: Question 4 Let f(x, y) = 2x4+ y4. Find the slope of the surface z = f(x, y) in the x-direction at…

A: The given function is: fx, y=2x4+y4 To find the slope of the surface z=f(x,y) in the x-direction at…

Q: Write the log equation as an exponential equation. You do not need to solve for x. In (4x + 8) = x+5

A: The given equation is: ln4x+8=x+5 To write the log equation as an exponential equation.

Q: Find the area between the curve and the x-axis for the function f(x)=³- on [0, 3] 2 O 0.25 O 16 O…

A: Given query is to find the area under the curve.

Q: Find COS X 2+ sinx dx

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Q: 2) Air is being pumped into a spherical balloon at a rate of 4.5 cubic feet per minute. Find the…

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Q: Find an equation for the line that is tangent to the curve y = 2x³ - 2x at the point (-1,0). The…

A: Given query is to find the equation of the tangent.

Q: Suppose you need to find derivative of product of two functions. that is to find [f(x).g(x)]' One…

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Q: The table gives the projected number of workers in various categories in Springfield in 2020. If one…

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Q: If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) =…

A: Given that:- u(x) = f(g(x)) v(x) = g(f(x)) w(x) = g(g(x)).

Q: Find the derivative of the function. f(x) = (4x + 5)(5x − 6)

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Q: Let f(x)=x^3−4 Estimate the following to within two decimal places by using small enough intervals.…

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Q: Evaluate 00 O 1/2 O 1/4 1 S'islar. -1

A: S=∫-11xdx

Q: Use implicit differentiation to evaluate az/ax at (1, −2, 1) if x³z − 3xy² – (yz)³ = -1 -

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Q: 27. y = cos x, a = π 6 dx = 0.014

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Q: 2 What is the angle formed by the vectors 1 syntax like 3*pi/4.) and ? (Express the answer in…

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Q: Use the Linear Approximation to estimate the value. Compare with the value given by a calculator.…

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Q: 1: Evaluate the following derivative: (VZx √1-√x y = √2x

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Q: An initial population of 3200 increases by 12% each year. How long will it take for the population…

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Q: Evaluate the following integral using partial fractions. J 52+3 x² + 2x - 3 dx

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Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

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Q: Q2: y" +9y = et Where y(0)=0 and y'(0)=0

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Q: Draw the following graph on the interval 5T 2 y-3 sin (3(2-)) +2.5 M&M

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Q: Find f’’(x) of F(x)= (X^2)/(1+2x)

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Q: The question below is based on the following four sets of data-pairs: (1) A and B, (2) C and D, (3)…

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Q: e the graph to find the following limits d function value. lim f(x) →3 lim f(x) lim f(x) (3) Find…

A: Given query is to find indicated limits.

Q: x Evaluate *f(u) du f(u) du if f(x) = 5. 4.9 O 5x−4.9 O 5x + 24.5 + O 5x + 4.9 O 5x24.5

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Q: B. Given any two positive numbers x and y, we define their geometric, harmonic, and arithmetic means…

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Q: Find equations of the tangent lines to the curve y = x + 1 that are parallel to the linex - 2y = 4.…

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Q: Show what is the surface of revolution obtained by revolving the equation 3y = 5z² around: a) y-axes…

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Q: Use implicit differentiation to find az/ax if x²₂² - 2xyz + y²z³ = 12. 2xz - 2yz³ 2x² - 2xy + 3y²z²…

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Q: Using partial derivatives, which one is equivalent to dz/dt, given z = x² + 3xy + 5y²; x = sin t, y…

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Q: Find the acute angle (in degrees) between the planes -−3x – 2y + 2z = 9 and 2x − y + z = 2.

A: Given planes:- P1: -3x-2y+2z=9P2:2x-y+z=2

Q: Find the center of mass of a thin plate of covering the region between the x-axis and the curve…

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Q: Show that u(x, y) = e* cos y + 2e* sin y + e* cos y + 2e* sin y satisfies the equation ²² + ax² dy²…

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