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Q: QUESTION 4 The graph below corresponds to which of the following o f(x) = (x+5)² c(x) = (x³ + 6) –1 ...

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Q: Prove that lim (2a2 + 3r + 6) = 5 using the e, 8 definition of a limit. %3D a -1

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Q: 1- 2x Prove that lim = -1 using the e, d definition of a limit. 5

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Q: Let g(x)= 5 - 5x + 4x2 then the expression (g(x+h) - g(x))/h can be written as Ah + Bx + C, where A,...

A: Given: g(x)=5−5x+4x2

Q: Calculus Question

A: Given: P(principal amount)=$10,000 r(annual interest rate)=0.1x12/100          ( because monthly int...

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

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Q: zoom for a better view

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Q: Which order of differentiation enables one to calculate fxy faster:x first or y first? Try to answer...

A:      Definition used -                       Partial derivative -                       In partial d...

Q: Find the first partial derivatives of the function. z = 8 tan(xy) dz ay Need Help? Talk to a Tutor R...

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Q: Evaluate the integral. (Use C for the constant of integration.) 2 dx

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Q: Simplify (assume X>0) √(48x3) / √(3x)

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Q: A given bacteria culture initially contains 2500 bacteria and doubles every half hour. The number of...

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Q: Determine the centroid bounded by the parabolas x=y^2 and x^2=-8y

A: Consider the given equation x2=-8yas, y=-x28 And y2=x then, y=x.Then, x=-x28x4-64x=0x=0,4 Thus, the ...

Q: Families of Functions A family of functions is given. In parts (a) and (b) graph all the given membe...

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Q: a. Find the local extrema of each function on the given interval, andsay where they occur.b. Graph t...

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Q: Evaluate ∫sec3 x dx.

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Q: Partial derivatives Find the first partial derivatives of the following functions. g(x, y) = cos5 (x...

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Q: The question is attached

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Q: Find the slope of the graph of the equation at the given point. (If an answer is undefined, enter UN...

A: The given curve is,  x2-y2=25 To find the slope of the given curve at (5,0) The slope of the functio...

Q: attached

A: The given Integral is ∫85t25t2-25dt

Q: Use the functions f(x) = (1/8) x − 3 and g(x) = x3 to find the given value          ( f −1 ∘ f −1)(−...

A: Given functions are fx=18x-3 and gx=x3. We have to find value of f-1o f1-2 We will find inverse of f...

Q: question is in picture below

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Q: 5. Solve for y. Your answer should be EXACT (no decimals). (hint: treat as a quadratic) e2y – 7ey + ...

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Q: Use the Table of Integrals to evaluate the integral.

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Q: We are standing on the top of a 1520 feet tall building and launch a small object upward. The object...

A: Given the vertical position of the object , measured in feet after t seconds is, ht=-16t2+224t+1520

Q: Consider the geometric sequence: -5, 10, -20, 40, ........Solve, Find the sum of the first ten terms...

A: The geometric sequence is -5, 10, -20, 40, ...   To find: Sum of the first ten terms of the sequence

Q: Let if x 3 - (a) Evaluate each limit, if it exists. (i) lim f(x) (ii) lim f(x) (iii) lim f(x) (iv) l...

A: Given function is fx=-x3-xif x<0  if 0≤x<3x-32   if x>3 (a) We have to evaluate limit of th...

Q: Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.

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Q: Use the Product Rule twice to find a formula for (fg)" in terms of f and g and their first and secon...

A: Product rule in derivative:  [A(x).B(x)]' = A(x).B'(x) + A'(x).B(x)

Q: Evaluate the definite integral. Use a graphing utility to verify your result. (Round your answer to ...

A: The given integral is ∫0π2xsin2xdx. Integration by parts: ∫uv=u∫v-∫u'∫v Using the method of integrat...

Q: Find a fundamental matrix of the systems in, then apply Eq. mentioned in the Attachement, to find a ...

A: We have given system of equation X'=3-111X,            X0=10      

Q: Trigonometric limits Use Theorem 3.10 to evaluate the following limits.

A: Given that limθ→0cos2θ-1θ. Compute the limit as follows.  

Q: Compute the following double integral over the indicated rectangle (a) by integrating with respect t...

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Q: Define the term convergence?

A: According to the question, we have to define the term convergence. Basically convergent sequence is ...

Q: The area of the region in the xy-plane enclosed by the x-axis, the curve y = f(x), f(x) 2 0, and the...

A: given: a function y=f(x), f(x)≥0. the area of the region in the xy plane enclosed by the curve y=f(x...

Q: Calculus Question

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Q: Show that if a>-1 and b>a+1 , then the followingintegral is convergent.

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Q: Calculate the present value PV (in dollars) of an investment that will be worth $1,000 at the stated...

A: Given, Amount (A) =$1000 Time (T) =6 years Rate (r) =5.1% per years For the compounded quarterly int...

Q: Find the derivative of the function. f (x) = 1/ ( 1+ x 2  )

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Q: Verify that the given function is a solution of the differential equation that follows it. Assume C,...

A: given: the function yx=C1e-x+C2ex the differential equation is y'(x)-y(x)=0

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.