1. Find the range of the given function: y=x² + 3x-4 Oy≤-6.25 y≤6.25 All Real Numbers y≥-6.25

Q: For the function f(x) = 3 - (x + 1)³, at the point (-1,3) - === O a. f has a relative maximum. O b.…

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Q: Given that the function f(x)=x²-2x+1 İS continuous on [0,2] and differentiable on (0,2), which of…

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Q: If f(t) = = (t² + 2t + 5) (7t² + 2), find ƒ’(t). Find f'(5).

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Q: Repeat the approximation using left endpoints. Ln =

A: Given f( x ) = 1x + 3 [ -2 , 3 ]

Q: Question 8 Find f'(x) if f (x) = log (cot 8x). 8 tan 8x In 6 - csc² 8x tan 8x In 6 8 csc 8x sec 8x…

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Q: 2. What is the second derivative of f(x) = - ²x³²x²+6? f"(x) = 5x² - ²³√x f"(x) = 10x + √√√x+6 a. b.…

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Q: If ƒ (x) = x³ − 3x + 5, find (ƒ−¹)′ (x) at x = f (2).

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Q: sinx-x x² n- 0 ng limits (apply L'Hospital" Int -; b) lim: ; c) lim x-1

A: Topic:- application of derivatives and calculus

Q: Find parametric equations for line that is tangent to the curve x = cost, y = sin t, z = t at the…

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: f(x)=64² +3 g(x) = 45+2 h(z) = 16 (1024)

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Q: Exercise 1. Tell whether the following sets are bounded from below and/or from above, specifying…

A: The given set is C=n−1n: n∈ℕ\0

Q: Select which of the following statements are valid results of multiplying the output of a function…

A: Given statement →when we multiplying output of a function by a constant a

Q: Prove the identity. (1- cos x)(1+ cos x) = 1 1+cot’x 2

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Q: rydz, where C' is g 5t, and 0 ≤ t ≤1

A: We have to choose the correct option from the given options according to the given information

Q: y T Q P R X n the figure above, line T is tangent to the graph of y = at point P, with bordinates…

A: To solve the following problem

Q: 4. Let s(t) = -5² + 40t be the position equation for a rock thrown upwards. At what time t, in…

A: Let's find time t to rock change directions.

Q: Find the average rate of change of the function f(x) Average rate of change Give an exact answer. =…

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Q: Find the cross product u x 7 where u = i +9j +5k i +9j +5k and = (8,- 4, 3). and ü xü =

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Q: 2 2xy dy = y² – 2x³ dx

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Q: The velocity of an object (in km per minute) t minutes after it begins moving along the positive…

A: The integral of a velocity function represents the displacement of the object.

Q: 2) Solve dy 4x " x2+342 3x² + y²

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Q: 04 * Find the equation of the line through (9, 2) with slope -2/3. Oy=-2/3 (x-9) + 2 or y = -2/3x +…

A: Given  line passes through x1,y1=9,2andslope (m)=-23

Q: hello, the actual answer should be only B and not A, yet i don't know why. please help

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Q: Find the particular solution of the differential equation y′–xey=2ey, given the initial condition,…

A: We can solve the given differential equation by using the variable separable method.

Q: Given that the distance in feet that a car moves in t seconds is given by d(t) = 4t2. Find the…

A: Given: d(t)= 4t2  when t= 15

Q: 7. The volume of the paralleliped with corresponding vectors (2, 1,0), (-1,2,2) and (0, -2,1

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Q: 1. The position function of an object moving horizontally along a straight line as a function of…

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Q: Question 1: F(t)= -{³ (a) 5. 2t+1 (b) 500-1500 t-1 The amount of money raised during a fund-raising…

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Q: Given a 2-dimensional function T(x, y) = 3y² + sin(x) answer the following a) find the expression…

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Q: 5. (- The length of a rectangle is increasing at the rate of 4ft/hr, and the width of the rectangle…

A: As we know that, The expression for the perimeter of the rectangle is: P=2l+b Where l is the length…

Q: A particle's acceleration is given by the expression a(t) = 2t3 m/s². The particle was measured to…

A: we need to find the velocity and position of the particle.

Q: The function given by f(x) = x³+4x² + 1 defined on the interval [-3, 2] has absolute maximum of

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Q: On which intervals is the graph of f(x)=2x4-12x² concave up? None of the choices. (1,+∞) only (-∞,…

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Q: State whether the following is true or false by differentiation. 1 [cos²(x) dx = x + ¹/ sin(2x) + C…

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Q: The vector w = ai + bj is perpendicular to the line ax + by = c and parallel to the line bx - ay =…

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Q: X√ хр. т-х а- by substitution b. by integral by parts

A: Topic:- application of integration

Q: f(x)=x^3+6x^2+3x+18 by factoring (use grouping) and using Cardano's formula.

A: f(x) = x3 + 6x2 + 3x + 18 f(x) = (x + 6)x2 + 3(x + 6) f(x) = (x + 6)(x2 + 3) The roots of f(x) = 0…

Q: The population of a town is f(x) = 3x - 11x + 240 people after x weeks (for 0 ≤ x ≤ 20). (a) Find…

A: A detailed solution is given below.

Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. Enter…

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Q: Solve the initial value problem.. (tan (@y) - 4)dx + (8x sec ²(By) + -] dy = 0, y(0) = 1 The…

A: Given differential equation ( tan( 8y ) - 4 )dx + ( 8xsec2( 8y ) + 1y )dy = 0 Mdx + Ndy = 0

Q: Question 2 A y B Hence, calculate the size of the shaded area R X Diagram not to scale- The above…

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Q: 3. The figure on the right side shows the circumscribed (big circle) and inscribed (small circle)…

A: given that,

Q: Of all possible right triangles with area 1, determine the one with the smallest hypotenuse.

A: This is an optimization problem, we find the critical points and use second derivative test.

Q: Write the end behavior for the graph

A: NOTE: Refresh your page if you can't see any equations. . from the graph, we can write the end…

Q: Which integral computer the volume of the solid bounded by 2 = 4-x² - y² and the xy-plane in…

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Q: Find the average rate of change of the function f(x) = Average rate of change = Give exact answer!…

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Q: What is the volume of solid generated when area bounded by y=x, y-axis and y=2 is revolved about…

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Q: Consider a function f(x) whose derivative f ′ (x) is given below. Find (i) all critical values, (ii)…

A: Given f'(x)=(x−2)3(x−1)2(x+1)

Q: For the function v (t) = 4t² - 6t+2, determine the value(s) of t on the closed interval [0, 3] where…

A: INTRODUCTION The Average Rate of Change function is defined as the average rate at which one…