5. Is the given function continuous at x=3 ? Justify your answer. Also decide, Is the function continuous for all real numbers x ? g(x) = (x² + 2x - 33, x² - 6x +9 x-3 if x ≤ 3 if x > 3

Q: The graph of a function is shown together with the tangent line at a point P. y 6+ 5 4 3 2 1 1 2 3 4…

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Q: b/ by using Chain Rule, the derivative of - sin 2t) is g(t) = tan (5

A: Solution

Q: Find a polynomial function with the zeros -2,3,5 whose graph passes through (7,144) f(x)=

A: Given, Zeros= -2,3,5 We know that polynomial function with three zeros a b and c is given by, f(x)=…

Q: Find the nth term of the arithmetic sequence whose initial term is a₁ = 4 and common difference is…

A: The nth term of the arithmetic sequence is given byan=a1+(n-1).d         Equation 1wherea1=first…

Q: Evaluate the following, where the upper limit is pi/2 and the lower limit is 0: ∫sin9θcos5θdθ

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Q: 21. If f(x) dx = A) 1. 3 and B) 2. f2f(x) dx = 20, then ₂ f(x) dx = C) 7. D) 13. E) 23.

A: 21. We have, ∫12fxdx = 3∫152fxdx = 20 To evaluate: The value of ∫25fxdx

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Q: Suppose that functions f and g and their derivatives with respect to x have the values shown to the…

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Q: 3 =-=—= x³. - 4x² + 16x + 14 with tangent lines parallel to the line 20x - 5y = 2. Find all points…

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Q: y" + 6y' + 9y = 16e¯* cos 2x

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Q: Let f(x)=3x+8, x₁ = 2, X₂ = 5, x3 = 8, x4 = 11, and Ax=3. 4 (8) Find Σ 1 (x) Δ.Χ. i=1 (b) The sum in…

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Q: 12. Let f(x) = -x² and g(x)=1/√√x. Find formulas for fog and go f and state the domain of each…

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Q: A = [3 2 01 00 67 -2, B= -1 2 71 053 006

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Q: 45° IIDII=23

A: To Find: the component form of vector with magnitude and angle

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Q: where is the answer in other numbers

A: Note: As per our company guidelines we are supposed to answer the first question with 3 sub-parts…

Q: dr=-4 tdt, when t=0, r=ro 0 r

A: We can find the particular solution in the below steps.

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A: Topic:- application of integration

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A: Our Aim is to solve the question-(8) in which our aim is to evaluate the integral given…

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A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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A: Initial position ( 0 , 5 ) which means particle has already covered π2

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Q: [50 07 -3 204-4] 02 0 1-530 0 0 -3 -6 222 3 2

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Q: Thank you but what about part d: which asks to solve f(1) ?

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Q: 02 01 Q3 Q4 05 Q6 07 Q8 09 Q10 Q13 Q14 Q15 The trigonometric substination to evaluate the integral…

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Q: Determine the g" ty T solution 2 the of given sin falt; y/o) = 10 y 10) = 0 77

A: The given differential equation is; y''+y=sqrt(2) Sin(sqrt(2)t), y(0)=10, y'(0)=0.

Q: 108 45. 765432 1 -1 y Chapter 2 Differentia f + 1 2 3 4 5 6 7 X 46. yd.

A:

Q: Evaluate the integral when x > 0 Answer: [n(x² + + 15x +36) dx.

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Q: Find the volume of the solid bounded by the paraboloid z = 4-², the cylinder r = 1 and the polar…

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Q: 11. Find the sum of the rectangle areas. 14 12 10 8 6 4 2 O 3 f(x)= 6 24 X 6 2

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Q: 7. Find the area under the first arch of the curve y = x sinx.

A: I have stated the used formulas in the solution

Q: 4. What are the values of the following infinite series? 1 3+ 1 2 + 4 5 —— 1 1 1 + + 27 243 + 5 4 25…

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Q: After Julia has driven for a quarter of an hour, she was 170 miles east from Denver. After driving…

A: Given that after Julia has driven for a quarter of an hour, she was 170 miles east from Denver. So,…

Q: Consider the vector field: V(x,y,z) = (10xy+3, f(x)-7, 0), where f(x) is some function. a) Find…

A: Please see the below pictures for detailed solution.

Q: 2. Sketch the graph of f(x) = sin(x) on [0, π]. Estimate the average value of f on this interval,…

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Q: 7. lim Z-0 cos²(y+z)-cos² y z A) cos² y. B) 2 sin y cos y. c) 2 cosy. D) - sin(2y). E) cos(2y).

A: L'Hopital's rule is used. Chain rule is used to find the derivative.

Q: Sketch the graph of the function by first making a table of values. f(x) = 13x - 3| X -5 -2 0 1 2 5…

A: Given function:- fx=3x-3

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Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: Slope of a curve y=f(x) at the point (a,b) is given by dydxx=a.

Q: Suppose that the function g is defined, for all real numbers, as follows. g(x) = -(x + 1)²+1 if-2…

A: find the function g(x) value at indicated x value.

Q: 2 Here is a graph of f(x) = x² and the line tangent to f(x) at (a,f(a)). The equation of the tangent…

A: Topic- Parabola and derivatives Slope of function  f(x) at x= a  is m=f'(a) and equation of tangent…

Q: 1 7. f(x) = √√√1 + √1 - x, at x = ² 4

A: Chain rule of differentiation is used.

Q: Jes − 4y = sinh x

A: Given: y''-4y=sinhx

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Q: 1. Evaluate the limit algebraically if they exist. The limit as of x approaches 3, square root of x…

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A: Linear Differential Equation: A differential Equation that is free from the product of dependent…

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A: Note:- As per our company guidelines we are suppose to answer only first three subparts. kindly…

Q: K The function f(x) = 1.1x³-32x² +262x+ 551 below models the number of discharges from the military,…

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Q: Estimate the indicated derivative by any method. (Round your answer to three decimal places.) dy y =…

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