-3 Let f be a continuous function such that f(x) dx = -6 and 10 10 1 f(x) dx 3. What is the value of dx? -3

Q: x+2 x<2 1) Let f(x)={ ax² – bx+3, ; 2sx<3 x 23 2x-a+b Find the values of the constants a and b given…

A: Here I am attaching image so that you understand each and every step.

Q: B-Test and proof the function So (x In x)² dx

A: ∫01(x logx)2dx=∫01x2 (log x)2dx use integral by parts, ∫udv=uv-∫vdu u=(logx)2…

Q: [2-x², x20 Given f(x) = , find the value c so that f(x) will be continuous at all values. x<0 x +C

A: Given that: f(x)=2-x2,    x≥0x+c,      x&lt;0   NOTE: As per our answering guidelines, we can only…

Q: 9. If f(5) = 10, f ' is continuous, and f '(x) dx = 15 18, what is the value of f(6)? %3D f(6) =

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Q: 16 8 If f is continuous and f(x) dx = 10, find f(2x) dx.

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Q: The derivative of the function f(x) =x ln x is: a. f'(x) = In x +1 b. f'(x) = ln x +. c. f"(x)= In x…

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Q: Ql.a- for what value of (k) is the function y= f(x) continuous at x=2 V7x + 2- V6x +4 -2 sx and x #…

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Q: 5. What is the derivative of 2x*? A. 8x3 В. 2 С. х D. 0 6. Consider the function f(x)=|x-21 at x-2…

A: Since you have posted multiple questions i can do first three question as per our company guidelines…

Q: 3. Consider the function for x +0 f(x) = for x = 0. (a) Would you expect S f(x) dx to be defined?…

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Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: 67. If f is continuous and f(x) dx = 10, find f(2x) dx

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Q: Sx' - 3, xS2 lx² +1, x>2 a. Is h continuous at x = 2? b. Is h differentiable at x = 2? 2. Given that…

A: A function is continuous at a point if the limit of a function at that point is equal to the value…

Q: x² – 16 tate why f(x) is continuous on [1, 2]. x² – 9

A: f(x) is continuous on [a,b] if and only if  1. ∀x0∈(a,b)⊆R, limx→x0f(x)=f(x0) 2. limx→a+f(x)=f(a)…

Q: 6. f(x) dx = 2, find If f is continuous and xf(x2) dx.

A: given f is continuous and ∫09 f( n) dx = 2 we have to find ∫03 xf (x3) dx = ? we solve this by the…

Q: 2- [10 points] Find the derivative dy/dx if y=3x +(5x ) (A) y=3°x +375 x² (B) y=3°*. 5 n 3+375x? (C)…

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Q: xf"(x) dx. Suppose that f(1) = 3, f(4) = 6, f'(1) = 6, f'(4) = 4, and f" is continuous. Find the…

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, oo).…

A: Given,           Let f(x) be a function that is defined and has a continuous derivative on the…

Q: V². Find the derivative of f(x) = In x² +1 %3D x(2r - 1)2

A: Derivative: f(x)=lnx2+1x(2x3-1)2ln(mn)=ln m-ln nln(x2+1)=12ln(x2+1)

Q: ind the linearization of the function given below at the specified point. f(x) = 5 In(x) at a = 1…

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Q: f (x) dx = 7 The function f has a continuous derivative. If f0) = 1, (2) = 5 and x. f' (x) dx what…

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Q: (c) A non-constant function f : [0, 1] → R such that f(x) > 0 for any x e [0, 1] but | f(x)dx = 0.…

A: In the given question we have to find the  function the function f(x) s.t f:[0,1]→ℝ s.t…

Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: V4+x-2 If f(x) = ,x*0 be continuous at x = 0, then f(0) = 1/2 1/4 3/2

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Q: Suppose y is a function of x. Find dy/dx. (a) g(x) = x + 1/x − 1 (using the definition

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Q: (c) Let g : R → R be a continuous function such that +5x-9 g(t) dt = –3x . Help Willow find the…

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Q: 1 If F(x)= - 0 1+ex -X e (1+e¯x)2 X- (1+e-x)

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Q: function f(x) such that f'(x) = (2x – 1)e²“. O Find the interval/s on which ƒ is increasing /…

A: Explanation: Given that,                          find the critical points to put the f'(x) = 0…

Q: 1.Find the derivative a. f(x) =x' In x b. f(x) = (x'+x-1)' %3D c. f(x) = 4e*- x %3D

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: A function y = f(x) is continuous and differentiable on the interval (0, 7). If f(x) dx = 13, f(1) =…

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Q: lim f(k+h)+f(k) h→0 ds Q3) Using the definition calculate the derivatives h dk 1 S= k – k of the…

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Q: Find the derivative of the function. f (x) :f(a) D 0 and f' (a) = - 3 Find F' (a) given that F(x) =…

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Q: 3. Consider the function f(x) = e¯*. 4x2 – 2 (a) Show that the second derivative is f"(x) (b) Find…

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Q: 2 2x +1 Let f(x) =- |- log, (x² + + 1) • (b* - 5b +3)x +c. If f(x)isa tan decreasing function of x…

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Q: (c) Does there necessarily exist a differentiable function h with 0 < h(x) <1 and E = {x : h(x) = 0}…

A: Sol:in the given question we have to tell about the differentiable function f(x)s.t whose range is…

Q: a) For the function f(x) =1–3x² , find f'(a) at a =-1 by using the definition of derivative. (a + bx…

A: Integration means addition. It is used for adding a continuous function that cannot be added by…

Q: 10 If f is a continuous function and F'(x)=f(x) for all x € R, then dx=? @2[F(5) – F(1)] ®2[F(10) –…

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Q: (x³ + bx + a, xs-1 lbx? - Let f(x) = .Then the values of a and b so that the %3D -a, x >-1…

A: The function is: f(x)=x3+bx+a, x≤-1bx2-a,      x&gt;-1 So, the function is continuous at x=-1 if…

Q: 7. If f(4) f '(x) dx = 15, what is the value of f(7)? 14 11, f'is continuous, and %3D f(7) =

A: Given

Q: x20 is continuous at x-0, then a = a+sinx If the function f(x): 2+2acosx x<0 a. 1 b. -1 O c. 2 d. -2

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Q: (a) Find the derivative of y = f(x) =2x+1 using this definition f (x+h)-f(x) f'(x)= lim h (b) If x…

A: Differentiate above function with respect to x

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: Given:fx=cos xxn for n=1,2,3,4Formula:ddxuv=vu'-uv'v2

Q: (a) Find the first and second derivatives of the following function (1² + x)(x² – x + 1) f(x) = %3D…

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Q: 1. What is dx [the function is f(x) = 1]?

A: To evaluate:

Q: dx For = In[F(x)]+C•What is f(/3) if C = 0? (x+x³) (x Tan-lx+ 1) -1 + - - 3. -1 + - + S-is-isS

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Q: Find the derivative of f (2) = xe 2 o f (2) = e * (e – 22) z- O f (x) = x°e-2# (;- 2) O (E) None of…

A: The product rule of differentiation states that d dxfg=fdgdx+gdfdx, where f,g are functions of x.…

Q: x-1 for x 1 x -1 show that flx) is continuous at x = 1 !3! for x 1,

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Q: Can you help step by step please?

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Q: Use differentials and the graph of f to approximate    (a) f (1.9) and (b) f (2.04).

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Q: 4. Using the expression (x + Ax)² = x" + nx-Ax +n(n – 1)x"-²Ax² + + Ax" ... prove that if f = ax"…

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Q: (Аx2 + 2Bх — 12 х 2 everywhere.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.