Evaluate the limit t3 – t lim t→1 t2 – 1

Q: 3. For what values of x does the graph of f (x) = x³ + 3x2 +x + 3 have a horizontal tangent.

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Q: 3.) y tanʼxdx +ln* ydy = 0 dy_ (y?+4) Inx In (y?+4)Y 5) dx

A: y tan2x  dx + ln4y dy = 0∫-tan2x  dx =∫ ln4yy dy∫(1 - sec2x) dx  = ∫ t4 dt   (where, t = ln y)Hence,...

Q: (3x2-7)* y = (3x2+5)4

A: Given:- y=(3x2-7)4 /(3x2+5)4 To find:- Derivative of given function

Q: -S; (4vw) dw

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Q: Now recall the general version of the power rule, where n is any real number. d = nx" – 1 dx Applyin...

A: Basic derivative problem

Q: 3.2 2. 3t (t 8-4れt。75 ニ

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Q: 2. Given f(x) = 3x – 2 and g(x) = +, find each of the following: (a) (f o g) (z) (b) (go f) (z)

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Q: (x² – 3 if x<2 5-x if x22 Sketch the graph of the piecewise defined function: g(x)=<

A: The given function is:

Q: 4² – y² +25:² = 100 %3D

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Q: 4. -6 -3 -3 -2 -1/ The graph above is a transformation of the function x² Write an equation for the ...

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Q: Find the slope of the function's graph at the given point. Function: f(x) = x² + 1 Point of the f(x)...

A: We have to find slope of function.

Q: 4x3+3x2- 30x-33 da Consider the indefinite integral x2 - 9 Then the integrand decomposes into the fo...

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Q: (a) lim (3xª + 2x² - x + 1) X-2 PIE

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

Q: e is an angle in standard position with T(-20, -21) on its terminal ray. Find sing O-21/29 21/29 -20...

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Q: 13 A spoke of a wheel makes 32 revolutions while the wheel is going 425 feet. Find the diameter of ...

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Q: Find // y dV, where E is the solid bounded by the parabolic cylinder z = x? and E the planes y O and...

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Q: = 1. Find the general term of the sequence, starting with n = Determine whether the sequence converg...

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Q: 2. Solve the system by Gauss elimination: х-Зу+z%3D1 2х- у+2z %3D2 x+2y– 3z = –1

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Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what ...

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Q: Verify F(x,y,z) = (2y + z )î + (x – z)ĵ + (y – z )k taken over a triangle cut from the plane x+ y+z ...

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Q: Differentiate the following functions. No need to simplify. a. f(x) 1 V6x + 5° + In(a*) = 7x7

A: We have to find derivative of f(x)

Q: 25. - lim (tan x)*om

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Q: DeAndre and Leah are making origami cranes. Their goal is to complete 1,000 cranes by the end of the...

A: We have to solve given questions on the basics of Given graph.

Q: x² 1. dx X=3 cos 0 /9—х2

A: Given that: ∫x29-x2dx

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Q: Consider the following sequence: {an} = {n – n² }, +00 Use an+1 – an to show that the given sequence...

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Q: 3 Select the function that is even. f(x) = 3sin(x) f(x) = 3tan(x) f(x) = 3cot(x) f(x) = 3cos(x)

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Q: Graph the linear function f(x) = - 4x. Identify if it is a constant function. Give the domain and ra...

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Q: 2 dse the Reimann Integral to evaluate S v'dv.

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Q: Let f(x, y) = x* + y* – 4xy. (a) Find all critical points of f. (b) For each critical point of f, us...

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Q: 4. lim f(x) = +o0, x-3- lim f(x) = -o 0- x-3+

A: here we have to draw the graph which satisfies the given conditions.

Q: Find the derivative. using chain rule 7 5. у %3 V1-14x2

A: The given function y=71-14x2

Q: Find the first three non-zero power series terms of each of the two linearly independent series solu...

A: we have to find the power series of y"=xy

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A: Given graph of a function f

Q: Evaluate the following function. 1. f(x) = 5x³ find f'(2) 2. f(x) = x³ + 3 find f'(3) 3. f(x) = x3 -...

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Q: Find for y =. (Sim %3D

A: y = x2/ e3x  

Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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Q: V. HIGHER DERIVATIVES AND CHAIN RULE (1+t)² 1. x = 2. y = x²(x – 1)°(2x – 5)² 3. f (x) = /1+ v1 – x ...

A: second derivative

Q: 1. If x'y-xy'+x' +y = 0 find y. %3D

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Q: Which of the following is the formula for finding the distance between two points on the coordinate ...

A: The formula for finding distance between two points (x1,y1) and (x2,y2) is, d=(x2-x1)2+(y2-y1)2 Opti...

Q: 9. Some weird shapes: For the following functions, use desmos to plot them dy for each of dx and com...

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Q: Provide a diagram where limx→a f(x) exists, f(a) is not defined and f(x) is not continuous at a. Wha...

A: A function f(x) has properties,limx→af(x) exits, f(a) is not definedfx is not continuous at x=a cont...

Q: A. Evaluate the following integrals. S(x² – 2)² dx 1.

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Q: ´sin x-sin x cos x lim x2

A: This can be evaluated as follows:

Q: Lesson 7 CL Activity # 1 #4 4. S(x) = (2x-6)* 4. f(x) =- (x+3) (2х-6)

A: We are asked to find the second deritives.

Q: Calculate the vector field flow g⟶ (x,y,z) = (y) î - (x) j + (x + y) k, counterclockwise, along the ...

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Q: Given the graphs of f(x) and g(x), determine the value of expressions below. y f(x) y = g(x) lim (f(...

A: From the given graph, we can find the following limits: limx→2f(x)=0  limx→2g(x)=0 limx→1g(x)=1 limx...

Q: Suppose that the total profit in hundreds of dollars from selling x items is given by P(x)=5x-5x+7. ...

A: Average rate of change of f(x) as x changes from a to b is given by, A(x) = [f(b) - f(a)]/(b - a)

Q: If R is the region bounded by the lines y = x,y=0,x= 1, evaluate the dxdy double integral S by chang...

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Q: Find the derivative of the function. G(z) = (1 – 6z)Vz? + 1 %3D G'(Z) = Need Help? Read It

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...