f(t) 2t − 4 + 3√t √t

Q: 2 (e^)² = e²x why rather than (e^)² = etz 2

A: To find the integral.

Q: Find the derivative of y with respect to x. 2 16x-1- y = cot -¹√₁ sec 4x,

A: Topic = Derivative

Q: 3. Suppose f: N→ N has the rule [n², f(n) = { n<8 n+1 n ≥ 5 Which of the following statements is…

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Q: 7. (D³ — 2D² − 5D + 6)y = 0; y = 1, Dy = −7, D²y = 1 when x = 0

A: The given equation is;  (D3-2D2-5D+6)y=0, y=1, Dy=-7, D2y=1 when x=0.

Q: A conical water tower with vertex down has a radius of 14 ft at the top and is 26 ft high. If water…

A: Given :   A conical water tower with vertex down has a radius of 14 ft at the top and is 26 ft high

Q: Use the limit definition of the derivative to answer the following questions about f(x) = 8x².…

A: Given f(x)=8x2 We know that (a+b)2=a2+b2+2ab

Q: 4. The graph of f'(x), the derivative of a function is shown at right. Which of the following…

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Q: Find f. f(0) = f "(0) = sin + cos 0, f(0) = 3, f'(0) f'(0) = 3 0

A: As per the instruction, we will be answering the first question. Given: So,               f…

Q: x=-1 y = ²+1 2 x=1 If the area of any region R is given by ff1dA, find the area of C

A: see below the answer and explanation

Q: Find the limit of f(x) + g(x) as x approaches c. lim f(x) X-C lim g(x) X-C Exercise (a) 17 4 Step 1…

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Q: 1. Sketch a region whose area is given by the following integrals. Then evaluate each integral by…

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Q: f do di

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Q: Find (f + g)(x), (ƒ − g)(x), (f · g)(x), and (4) (x) for each. 1. f(x) = x² + 4 g(x)=√x 2. f(x) = x²…

A: Given function:- fx=x2+4 ,gx=x fx=x2+x,gx=9x

Q: The graph of y = f(x) is shown. 10-9-8-7 -6 -5 -4 -3 -2 10 9 8 7 6 5 4 3 2 + -1 -2 -3 -4 -5 -6 -7 -8…

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Q: Let u = = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that the angle between u −…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the indicated one-sided limits of f, and determine the continuity of f at the indicated point.…

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Q: Consider the following vector: -E1₁ 2 2 Which vector has length 2 and the same direction as u? 200…

A: given  u=-122

Q: If the function f defined by I < 2, {32²-4, 222, is continuous everywhere on (-∞0, ∞o), what is the…

A: To find the functional value at x=1 if given function is continuous.

Q: Sketch a function that clearly satisfies all of the conditions below.

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Q: Use truth tables to check if the given pairs of formal propositions are logically equivalen and…

A: A detailed solution is given below.

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y…

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Q: Let lim f(x)=16. Use the limit rules to find the following limit. lim √f(x) lim √/1(x) = (Simplify…

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Q: Logarithm Rules log, xy = loga y log,x": log, b = log, b =

A: Given :logaxy=logaxy=logaxn=logab=logab=

Q: Find the rules for the composite functions fo g arld go f. f(x) = 4√x + 1; g(x) = x² + 5 fog = gof=

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Q: Find each x-value at which f is discontinuous and for each x-value, determine whether f is…

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Q: 6. (D² + 1)y = 10e* sin x

A: see below the answer and explanation

Q: lim In X-8 1-)-e X ex

A: Given limit limx→∞ [ ln( 1x ) - ex ]

Q: ons [2/2] [1.5/2] 3 4) (1/2) [1/1] 6/11 The graph below shows the relationship between the height of…

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Q: K Graph the hyperbola x² - y² =9. Give the domain, range, center, vertices, foci, and equations of…

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Q: Given that vector u has length 2, vector v has length 3, and the dot product of u and v is 1, what…

A: We need to find the value of 2u-v

Q: Find the integrating factor μ(x) of y' = 25x¹y +3 such that μ(0) = 1.

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Q: = a. Mtan f(a+h)-f(a) h a. Use the definition mtan = lim h→0 b. Determine an equation of the tangent…

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Q: Determine whether the following function is continuous at a. Use the continuity checklist to justify…

A: To determine whether the following function is continuous at a. fx=x-7; a=3

Q: Suppose that ?(?) is a function with ?(95)=76 and ?′(95)=6. Estimate ?(97.5).

A: To estimate the value of the function at given value of x.

Q: Consider the following graph of the function g. कोरि 0 -2 1 2 3 x ® From the given graph of g, state…

A: A function is said to be discontinuous at all those points where there is a break in its graph.

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 3x² + 11x - 4 lim X→-4…

A: let  A=limx→-43x2+11x-4x2-16if we put x=-4,  A=00 form there for use l'hopital rule ∂xn∂x=nxn-1∂…

Q: Consider vectors 3 u=-2 and v= What is the cosine of the angle between u and v? 16/0 3 10 3√14 0 2…

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Q: The parallelepiped with adjacent edges PQ. QR and PS with P(2.0,2).Q(-4,3,6). R(4,1,1) and S(0,4,3)…

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Q: Find the arc length of the curve below on the given interval. 3 1/3 4 y= 2x5/3. - +7 on [1,8]

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Q: Given f(x, y) = 5x¹ - 4x²y – 2y5, find fx(x, y) = fy(x, y) = fxx (x, y) = fxy(x, y) = fyy(x, y) =…

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Q: Use the second degree Taylor polynomial of f(x) = about to approximate your answer as a single…

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Q: Which of the following differential equations is separable?

A: A differential equation is called separable when it can be written in the form of dydx= f(x) g(y).…

Q: 8. Find the value of k in order for k cos" ( 10. Prove the identity sin x csc x + cotx ² (2) - 6/2 k…

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Q: Find the volume of the solid formed by rotating the region enclosed by 1x y=e¹x + 1, y = 0, x = = 0,…

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Q: -710 (-7 "divides" 0)

A: Given expression -7 | 0 what it means

Q: Differentiate the given function. y=x√√6x-1

A: Introduction To find the derivative of given function we have to use the following properties of…

Q: Find the unit rate. Del Monte Sweet Peas $1.42 for 14 oz. What is the cost for one ounce?

A: Here is the solution:

Q: Select the law which shows that the two propositions are logically equivalent. (¬p^ (rv¬q)) v (…

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Q: Which of the following integrals represents the volume of a unit sphere by integrating the volume of…

A: Let Volume = V Area = A

Q: Find y' and y". y' y" 11 = y = √x In(x) x¯(³)in(x) 2 x x

A: