Recent questions tagged graph

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Recall that one construction of the weight matrix for a graph on data points $\{ x_i \}_{i=1}^n$ is to use the Gaussian kernel $$W_{ij} = \begin{cases} \exp(-\Vert x_i - ...
111
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\( \int \frac{x}{x^{2}+4 x+5} d x \)
139
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\( \begin{array}{l}200 \% \times 200 \%=? \\ \begin{array}{ll}\text { A. } 40 & \text { C. } 4 \\ \text { B. } 400 \% & \text { D. } 0.4 \%\end{array}\end{array} \)
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Suppose that \( u \) is continuous on \( [a, b] \) and differentiable on \( (a, b) \). Then there is a point \( \xi \) in \( (a, b) \) such that\[u(b)-u(a)=u^{\prime}(\xi...
84
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Find the derivative of the function \( f(x) = x^3-4x+8\) from first principles
122
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Why is graph of sequence discrete?
86
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Evaluate the limit of \(f(x)=x^2-5x+6\) as \(x\) approaches \(3\)
66
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Evaluate: \( \frac{d y}{d x} \) if \( y=x^{2}-\frac{1}{2 x^{3}} \)
62
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Differentiate \( f(x) \) from first principles if \( f(x)=-2 x^{2}+3 \).
78
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Sketched below is the graph of \( g(x)=-2 x^{3}-3 x^{2}+12 x+20=-(2 x-5)(x+2)^{2} \)\( \mathrm{A} \) and \( \mathrm{T} \) are turning points of \( g \). A and \( \mathrm{...
66
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Determine \( f^{\prime}(x) \) from first principles if \( f(x)=-3 x^{2} \).Determine, using the rules of differentiation:\[\frac{d y}{d x} \text { if } y=\frac{\sqrt{x}}{...
110
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Explain why \(z1 \times z2 = (\bar{z1}\times z2 + z1 \times \bar{z2})/2\)
140
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What does \(5y – 1\) mean in words?
119
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If \( h(x)=\frac{x^{2}-1}{x+1} \), find \( h^{-1}(x) \)
168
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explain this \( X_{i, j}^{t+1}=\left\{\begin{array}{ll}X_{i, j}^{t} \times \exp ^{\left(\frac{-h}{\times \times T}\right)}, & \text { if } R_{2}<S T \\ X_{i, j}^{t}+Q \ti...
135
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Evaluate \( \sum_{k=7}^{17}(-2 k+14) \)
97
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Given: \( f(x)=5 x^{2}+6 x-7 \)1. Solve for \( x \) if \( f(x)=0 \) (correct to TWO decimal places).2. Hence, or otherwise, calculate the value of \( d \) for which \( 5 ...
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What is a point of inflection?
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From 30 to \( 90 \mathrm{~s} \),\[\begin{aligned}a & =\frac{d v}{d t} \\& =\frac{d}{d t}(-0.5 t+45) \\& =-0.5 \mathrm{~m} / \mathrm{s}^{2}\end{aligned}\]Displacement,\[s=...
288
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1 Determine \(f^{\prime}(x)\) from first principles if it is given \(f(x)=x^2-5\).2 Detcrmine \(\frac{d y}{d x}\) if:2.1 \(y=3 x^3+6 x^2+x-4\)2.2 \(y x-y=2 x^2-2 x \quad ...
265
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The value of \(y^{\prime} / x^{\prime}\) in terms of the angle 0 is given by
332
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What is \( 1 \div 2 \times 1 \) ?
345
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\( 6 \div 2(1+2)= \)
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\( \begin{array}{l}\text { If } x=5+2 \sqrt{6} \\ \text { Find } \sqrt{x}+\frac{1}{\sqrt{x}}\end{array} \)
277
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Work out the value of \(x\)
665
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Calculate the roots of the cubic equation \(x^3-8=0\), show all working. Use latex.
416
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How do you calculate the derivatives of trigonometric expressions?
282
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How do I compute the derivatives of functions that are explicitly given with some formula?
253
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On a graph, what is an x-coordinate?
409
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Does the mass of the object affect the falling speed?
254
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Suppose you are walking along the road and observe two cars. Car A starts from rest and travels along a straight road with a constant acceleration of 3 m/s2 until it reac...
353
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The diagram below shows the graphs of \(f(x)=x^2-2\) and \(h(x)=a x^2+b x+c\). The turning point of \(h\) is \(Q(-1 ; 4) . \mathrm{R}\) lies on \(f(x)\) and QR is paralle...
426
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A certain company sells \(x\) units of a product. Its profit in rands is given by: \(P(x)=-3(x-17)^2+560\).Write down the number of units that must be sold to earn a maxi...
342
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Given: the graph of \(k(x)=-x^2+3 x+10\) with turning point at \(D\). The graph of the straight line \(h(x)=m x+c\) passing through points \(B\) and \(C\) is also shown. ...
284
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The sketch shows the graph defined by \(f(x)=a x^2+b x+c\). Which of the following statements \((\boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}\) or \(\boldsymbol{D})\) i...
268
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Give the range and domain of the following graph.
280
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Determine the equations of the graph: \(y=2^{x-p}+q\)
210
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Calculate the values of \(g ; h ; i\) in the equation below\(y=g \cdot h^x+i\)
391
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Calculate the values of \(d ; e ; f\) in the equation below\(y=d x^2+e x+f\)
234
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Calculate the values of \(a; b; c\) in the equation below \(y=\dfrac{a}{x-b}+c\)
516
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The graph of \(f(x)=a x^2+b x+c\) and the straight-line \(g(x)\) are sketched below. A and B are the points of intersection of \(f\) and \(g\). A is also the turning poin...
218
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The graphs of \(f(x)=-x^2+7 x+8\) and \(g(x)=-3 x+24\) are sketched below. A and B are the \(x\)-intercepts of \(f\) and \(\mathrm{S}, \mathrm{T}\) and \(\mathrm{R}\) are...
230
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The graphs of \(f(x)=c^x+d\) and \(g(x)=\frac{a}{x+p}+q\) are sketched below. The graph \(f\) passes through the point \(B(2 ; 5)\) and the two graphs intersect at \(A(0 ...
275
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How do you find the equation of a parabola given its vertex and focus?
596
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What is a limit of a function?
297
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What is the formula for the perimeter of a triangle?
266
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What is the domain and range of the function $y = \frac{1}{x}$?
467
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What is the equation of the parabola with vertex at $(3,-2)$ and directrix $y=-1$?
282
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What is the equation of the circle with center $(5,3)$ and radius 8?
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