Find the limit 2 ·lim t²-16 t-4 t³-64 3

Q: Find an equation of the tangent plane at the given point: F(r, s): - (27²+¹), (-2,1) N ==

A: Given function:- Fr,s=-2r2s0.5+1s4

Q: Graphs of f(x) = 5x and g(x) = 5√ intersect at the points (0,0) and (1,5). The region between those…

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Q: ԱՆ JS 12x + 3y² dA R es x = y² and x = 9.

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Q: 2) f(x) = sin−¹(x + 1) + ½/ Table: y = sin ¹x Transformations: D: R: X

A: y= Sin-1x

Q: Find a function f such that  ∇f = 7e7x cos(3y)i − 3e7x sin(3y)j + z3k.   f(x, y, z) =

A: we need to find out the function f whose gradient is given.

Q: Set up but nit evaluate an integral for the area of the surface obtaining by rotating the curve y=…

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Q: If f(x) x+1 4x 3x + 5 13x + 5 3x + 3 13x + 1 3x + 2 and g(x) = 3x x + 3' then (gof)(x) is

A: given  f(x)=x+14x                        g(x)=3xx+3           gof(x)=g(f(x))

Q: (c) [(317+(31 sint)7) dt (d) ((e)i+e' cos(re)7) dt

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Q: Find the Imit using l'Hospital's Role x-3 (i) lim x+3√√x+1-2 (j) lim 1 - COS (k) lim (1-2x)¹/x x-0…

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Q: Use the particular solution method to solve y - y = 2e²

A: Given that  a first order linear differential equations and we find particular solution of this…

Q: 3. Consider f(x) = on the interval [6,14]. Verify f(x) satisfies the conditions of √x-5 the mean…

A: Suppose that a function f is continuous over a,b and that f is differentiable over a,b. Then, there…

Q: Work xx 0x28 28x² 0x³ 7 8 x56 Ox15

A: The given problem is solved below in detail.

Q: Find f. f"(x) = cos(x), f(0) = 3, f'(0) = 6, f"(0) = 4

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Q: Find the general solution of the differential equation xdy + (x^2- 2y)dx = 0. O y + (1/2)x^2= c O y…

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Q: A storage shed is to be built in the shape of a box with a square base. It is to have a volume of…

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Q: Use the chain rule to find the derivative of 6√10x8 + 8x7 Type your answer without fractional or…

A: Topic- Derivative of a function We are given f(x)=610x8+8x7Formulas used:chain rule:…

Q: Find the centroid (x, y) of the region that is contained in the right-half plane {(x, y) | x ≥ 0},…

A: As we know the expression for the centroid. x¯=1A∬xdydx and y¯=1A∬ydydx Where Area=A=∬dydx   From…

Q: 3. (a) Evaluate lim 818 3x¹ - 4x² + 7x - 1 -7x4+x³+4 (b) Determine the equation of horizontal…

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Q: Find dy by implicit differentiation. x² + x³y² + y²³²-6

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Q: The graph of the derivative of f(x) is shown below: 7+ 6 5 4 3 2 -7 -6 -5 #4 -3 -2 -1 -1 -2 -3 -4 -5…

A: Topic = Functions

Q: Given the function f(x) - A. Factor [Select] [Select] x(5x+5)(x-3) B. Find th x(5x+3)(x-5)…

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Q: (a) In(a + b) In(a)In(b) for all a,b > 0 OTrue False (b) In(a-b) In(a) + In(b) for all a,b>0 OTrue…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: dy For the equation, use implicit differentiation to find dx y5 - x² = 6

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Q: Let f(x) = = f'(x) = = /3x² + 3x + 2 2

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Q: b) r = 1 2sint+3cost

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Q: Suppose the derivative of the function y=f(x) is y'=(x-4)²(x-2). At what points, if any, does the…

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Q: 4 2 -5 -4 -3 -2 -1 -2 -4 -6 -8 -10+ 1 2 e function graphed above is: cave up on the interval(s) cave…

A: The function is concave up where -2<x<1.   The function is concave down where 1<x<5.

Q: nd the arc length along a circle of radius 14 units subtended by an angle of 160°. Round your answer…

A: Given query is to find the arc length.

Q: An open rectangular box (no top) is formed with a square base and rectangular sides so that the…

A: Solution is given below:

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? Give…

A: Given function: fx=x8/9 on the interval -8,9.

Q: ← Find the derivative of the function y = (5x+1)3³ (4x+1)-². dx 11

A: Given query is to find the derivative of the expression.

Q: Önsider the integral 9 S² = the integral is divergent, type an upper-case "D". Otherwise, evaluate…

A: Given query is to find the value of the integral.

Q: Let f(x) = x³ + 6x² (a) Use the definition of a derivative or the derivative rules to find ƒ'(x) =…

A: Given function:- fx=x3+6x2-96x+19

Q: 1 2. Find all critical numbers of ƒ(x) = x³ + x¹ −4x³+3. Classify each as a local max, local min, or…

A: On solving this we will get

Q: A. 8-24x C. Find the second В. 8х + 10-6х-4 8+ 24x−1 8+24x-5 D c. Y = 4x² + 10x + -5 Find derivative…

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

Q: Determine whether the Mean Value Theorem applies to the function on the given closed interval. If…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: 2x x²-1 For #5-12, f(x) = 5. Find all x-intercepts (also called zeros or roots) of f 6. Use a test…

A: we will find the required.

Q: Find three positive numbers x, y, and z that satisfy the given conditions. The sum is 72 and P =…

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Q: Find the derivative of y = √√4x³ – 7. dy √12x² dx dy dx dy dx dy dx = = = = ²1 (4x²³ - 7) + 3x²…

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Q: 2 10x The function f(x) = x²e¹⁰x is increasing on the interval and is decreasing on the interval The…

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Q: Find an equation of the tangent line to the curve at the point (, y()). Tangent line: y = y =…

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Q: Find the intercepts and asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes…

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Q: For the demand equation, use implicit differentiation to find dx p² + p + 9x = 120

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Q: Find the indicated limit. Make sure that you have an indeterminate form before you apply l'Hôpital's…

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Q: concentration of a drug t hours after being injected is given by C(t)= 0.3t / t2 +68 Find the time…

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Q: This is incorrcet. The graph is correct but p(x) and the minimum is incorrect

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Q: state the axioms that define a group.

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Q: What is f'(x) if f(x) = -? 40x5 ex

A: Given data, fx=40x5ex

Q: f(x) = 6x - 5 (a) Find the inverse function of f. f-¹(x) = + 5016 (b) Graph fand f-1 on the same set…

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Q: For the given function, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum…

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